熟知Stein流形是一个极其重要的流形,在Stein流形上有很多非常数的全纯函数.Cn就是一个Stein流形,所以在Stein流形上研究多元复分析是很自然的.积分表示方法是多元复分析的主要方法之一,它的主要优点是象单复变数的Cauchy积分公式一样便于估计.过去人们已经得到了许多Cn以及Stein流形逐块光滑强拟凸域上为解--方程所需的积分公式,由此也得到了一些(0,s)型微分形式的--方程解的H\"older估计和一致估计.C.Laurent-Thiebaut&amp;J.Leiterer[10]引进局部q-凸楔形,它是逐块光滑强拟凸域的拓广,从而得到了Cn上局部q-凸楔形的Cauchy-R...It is well known that a Stein manifold is a very important manifoldon which there are many nonconstant holomorphicfunctions.Cn is just a Stein manifold. So it is very natural toresearch into complex analysis in several variables on Steinmanifolds. The integral representation method is one of main methods of complex analysisin several variables. In the past, many integral formulas for solving the-e...学位：理学硕士院系专业：数学科学学院数学与应用数学系_基础数学学号：20042301

翁桂英

Xiamen University Institutional Repository

0/j 10384 6jj 0 j 200423012 UDC:/  1 e  hStein /o#[ q- ZfoEn ∂̄- zbnzUniform Estimates of Solutions of ∂̄-Equationson Local q-Convex Wedges in Stein Manifolds: ( >A',3;. 1 % C ,5B = . # ) $ 6 <-97+20 2 0 0 7 / 4 -9&"4* 2 0 0 7 / <85?20 2 0 0 7 / r3bn.p r _20074 4p厦门大学博硕士论文摘要库_5iss[4^ÆgrH9<X.1eh(ay  uv\W5IWd(ayhL%JXE<GaI5IWdSyh%G$Z16$(aC*[p\zYlh&N|~$a (H&): 6 q f厦门大学博硕士论文摘要库_5iss[4^!?KH9(a\X:ww1[ZU1eh_ww1[V<b!0[DR4.h!p?[V+1ehU_3Qs,w~=<t)hCl1T%\%Ms[V+1eh0i0l[Z+O^C!&8[V+1eh6Gp<0 1ehy: xU(_(1eh(_1  	y 6: xU(#V%2  	PyGvPdk0s ”√”	LH& fB 6 q f H& fB 6 q f厦门大学博硕士论文摘要库: 0\u . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1\u . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3  t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5ow Stein ,lR & . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9§1.1 Stein -m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9§1.2 ÆS' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10§1.3 QJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11ot Stein ,l X q- WlCkS1}L ∂̄- w_k . . 14§2.1 QJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14§2.2 !Y q- Xdmlr| Leray G . . . . . . . . . . . . . . . . . . . . . . . . . 18§2.3 !Y q- XdmlT2~M ∂̄- x`l . . . . . . . . . . . . . . . . . . . . 20o ∂̄- w_k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25§3.1 R H 	l<qldV7P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25§3.2 * λ  M m (m ≥ 1) jR . . . . . . . . . . . . . . . . . . . . . . . .35§3.3 * Range-Siu >|f ∂̄- x`lx . . . . . . . . . . . . .47\$\` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54厦门大学博硕士论文摘要库ContentsChinese Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1English Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Chapter 1. Stein manifolds and basic lemma . . . . . . . . . . . . . . . . . . . . . . . 9§1.1 Stein manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9§1.2 Basic lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10§1.3 Notation and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Chapter 2. Homotopy formulas and ∂̄-equation on localq-convex wedges in stein manifolds . . . . . . . . . . . . . . . . . . .14§2.1 Notation and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14§2.2 The definition of q-convex wedges and Leray map . . . . . 18§2.3 Homotopy formula and the solution of ∂̄-equationon local q-convex wedges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20Chapter 3. Uniform estimates of solutions of ∂̄-equations . . . . . . . .25§3.1 A first description of the singularity of the kernel of H 25§3.2 Estimation of operators of type m (m ≥ 1)by λ-free bounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35§3.3 Uniform estimates of solutions of ∂̄-equations by theRange-Siu trick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Acknowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54厦门大学博硕士论文摘要库Stein 	KB q- Rs	 ∂̄- /Y8	?T 1 u& Stein AFD+;x Stein uZt$2O*Wih* Cn JAF Stein 9Fx Stein u4H$m<6otB\Æ680)$m<6o/;0)A=/;W{<2* Cauchy Æ6OA81^UfU`DF ($Cn F Stein -_℄|K3Seu_9 ∂– 0[9&Æ6OXk= A (0, s) ℄6 ∂– 0[9 Hölder UoAUC.Laurent-Thiebaut &J.Leiterer[10] NBLC q- S=-_℄|K3SeX^n%  Cn uLC q- S Cauchy-Riemann 0[9AU(O [14] rT Hermitian }oSx [13]   Stein LC q- Su (r, s) ℄6OOo ∂- 0[9xkeuKrT C.Laurent–Thiebaut &J.Leiterer[10] 1o R.M.Range & Y.T.Siu[8]0) Stein uLC q- Su (r, s) ℄6 ∂̄- 0[9AUWg6q/; Cn uLC q- Su ∂̄- 0[9AUU^ Stein u'g# X A< n a Stein  D ⊂⊂ X AUA<x  Stein uAK'moj Stein <Mo<`MozaFI+;'mÆ'<x (O [14] NK!yNk Stein uLC q- S\wrT Hermitian }oSx [13], ;Kb O Leray Sy  Stein LC q- SuOOo ∂̄- 0[9O?g.;Æ6n%-! .;Æ6<uUX^LC q- S-_℄|K3SeX^9FOOZA4JK=x q- Su ∂̄-0[9AUo CR- WiUXuZ+;KTqOT C.Laurent-Thiebaut & J.Leiterer[10] 1rT Hermitian}oSx [13], FLC~L!yKb  Stein LC q- S厦门大学博硕士论文摘要库Stein 	KB q- Rs	 ∂̄- /Y8	?T 2u (r, s)(r > 0, s > 0) ℄6Æ66> H lAU\wrTR.M.Range & Y.T.Siu[8] 0)  Stein LC q- Su (r, s)  ∂̄- 0[9AUh Stein LC q- S Hermitian }SxAU厦门大学博硕士论文摘要库Stein 	KB q- Rs	 ∂̄- /Y8	?T 3ABSTRACTIt is well known that a Stein manifold is a very important manifold onwhich there are many nonconstant holomorphic functions. Cn is just a Steinmanifold. So it is very natural to research into complex analysis in several vari-ables on Stein manifolds. The integral representation method is one of mainmethods of complex analysis in several variables. In the past, many integralformulas for solving the ∂̄-equations on Cn and Stein manifolds were obtained.Based on these integral formulas, the Hölder estimates and uniform estimatesof solutions of the ∂̄–equations for (0, s) differential forms were also given.C. Laurent-Thiebaut & J. Leiterer[10] introduced local q-convex wedges in Cn,which are extensions of piecewise smooth pseudoconvex domains, obtained thehomotopy formula and the uniform estimates for the Cauchy-Riemann equa-tion on q-convex wedges in Cn. By using the Hermitian metric and Chernconnection[13], Tongde Zhong[14] obtained the homotopy formlas for (r, s) dif-ferential forms and solutions of ∂̄-equation on local q-convex wedges in Steinmanifolds. On the basis of [10,14], by means of the ideas of C. Laurent-Thiebaut & J. Leiterer[10] and trick of Range & Siu[8] , the author obtains theuniform estimates of the solutions of ∂̄-equations for (r, s) differential formson local q-convex wedges in Stein manifolds.The whole dissertation includes three chapters. The aim of this paperis to generalize the uniform estimates of solutions of ∂̄-equations on local q-convex wedges in Cn to Stein manifolds. Suppose that X is a Stein manifoldof complex dimension n and D ⊂⊂ X is an open set.In the first chapter, the author introduces some definitions, the basiclemma and notations on Stein manifolds, including a Stein manifold, the com-plex tangent bundle, the complex cotangent bundle, fibre, and the most im-portant basic lemma and so on.厦门大学博硕士论文摘要库Stein 	KB q- Rs	 ∂̄- /Y8	?T 4In the second chapter, the results of Tongde Zhong[14] are introduced.The local q-convex wedges in stein manifolds are defined. Then, by means ofthe Hermitian metric and Chern connection[13],Tongde Zhong[14] constructed aLeray map, and obtained the homotopy formulas and solutions of ∂̄-equationon local q-convex wedges in stein manifolds.The integral formula does notinvolve boundary integrals, so one can avoid complex estimates of the boundaryintegrals. Moreover, a local q-convex wedges in Stein manifolds is an extensionof piecewise smooth pseudoconvex domain, so the homotopy formula has itsgeneralization meaning, it has important applications in uniform estimates of∂̄-equation and holomorphic extension of CR-manifolds.In the third chapter,by means of the ideas of C. Laurent-Thiebaut and J.Leiterer[10], and by introducing the Hermitian metric and Chern connection[13]and using of the localization technique, the author admits some estimate ofthe integral operator H for (r, s)(r > 0, s > 0) differential forms on local q-convex wedges in Stein manifolds. Then by means of the trick of Range-Siutrick[8] the authors complicatedly calculate the uniform estimates of solutionsof ∂̄-equation on local q-convex wedges in Stein manifolds.Key words: Stein manifold; local q-convex wedge; Hermitian metric;Chern connection; uniform estimate.厦门大学博硕士论文摘要库Stein 	KB q- Rs	 ∂̄- /Y8	?T 5Stein .n"Z q- YenDm ∂̄- yamy ∗  t}y*0DADa%$m<6o,S	AD0A$m<6o4H/;/h<6od<q%$<2d<qA-L"K0,S *0PA"}y*0ldI7AX^/h6^.o}[9FyT}y*09Z0)zx 1831 5 Cauchy (} FD%C'%1% Cauchy Æ6O*0 JdÆ68x<6o$+;"BnuF 70 5yG.M.Henkin[1,2] o H.Grauert & I.Lieb[3] 6:  Cn ℄%$K3Seu ∂̄-0[9Æ6Ow$<2*Æ680)25(GgV_$m<6o/;0)A=/;W{2* Cauchy Æ6OA81^U& Cn ℄%$Wih*o℄|h*Æ68DOTDFZ($4H [1−6], Bn W.Koppelman[7] ^ 1967 5  Cn ℄%$ (0, s) ℄6 Koppelman OZY Cn ℄%$ (0, s) ℄6Æ68m=DFZ($4H [4−6]. 1970 5 G.M.Henkin[1] o H.Grauert & I.Lieb[3] U ! Cn ℄%$PZ℄|.;K3Seu ∂̄- 0[9B 4H 1973 5R.M.Range & Y.T.Siu[8] !yKb  Cn ℄%$PZ-_℄|.;K3Seu (0, s)  Koppelman-Leray-Norguet OD ∂̄- 0[9AU!^APZ-_℄|.;K3S$"H G.M.Henkin & E.M.Chirka[9] Kb  Koppelman-Leray-Norguet OD ∂̄- 0[9AU1993 5 C.Laurent-Thiebaut & J.Leiterer[10] Q{ AFY^ λ 2 " Leray Syn%  Cn $LC q- SuOOo ∂̄- 0*a[Y.==2* (*;9i 10571144) mvt.V$^E}Æ厦门大学博硕士论文摘要库Stein 	KB q- Rs	 ∂̄- /Y8	?T 6[9AU!^ q = n − 1, XKLC q- S-_℄|K3SeMkLC q- Sy8 Ajt^.e=$ G.M.Henkin &R.A.Airapetjan[11], A.Andreotti & H.Grauert[12] Æ^.OT^B CRM  Cauchy-Riemann 0[ CR- h*WiUXo ∂̄- uOmJ.P.Demaily & C.Laurant-Thiebaut [13] 4H Stein u (r, s) ℄6Æ6O=o Cn  (r, s) ℄6 Stein u (0, s) ℄6?O	?2	 Cn ℄%A8GT Euclid }M_k Euclid}?Wi2t?2}_ 9Q?2}iF J.P.Demaily &C.Laurant-Thiebaut [13] rT Hermitian }oSxQ{  Stein Y^ (r, s) ℄6x?2}tÆ6l  Stein u KoppelmanOo Koppelman-Leray-Norguet Oo ∂̄- 0[9	F12O+;xkeu(O [14] rT Hermitian }oSxQ{  Stein LCq- Su (r, s) ℄6x?2}tI*Æ6l  Stein LC q-SuOOo ∂̄-0[9jkO?gZ.;Æ6n%-! .;Æ6<uU;NÆ6l=?,Kx.;u%&KxSe/=ZgBWiUXiF2;B\!XÆ6OKb ∂̄- 0[B U!yKb  Cn ℄%$Z C2 .;K3SUoK3Seu ∂̄- 0[9PZ 1/2-Hölder U2;℄Ar Cn $.;2℄|o.;-_ C1 ℄|K3SeFK3S$"Hu ∂̄– 0[9PZAU [4−6]. 1970 5 G.M.Henkin[2] rTX Henkin o Ramirez Q{Æ6O  Cn u C2 K3SU ∂̄-0[9AU;N Hölder U=X G.M.Henkin & A.V.Romanov[15] 9#!^LC qS} f ∈ Bβn,r(D)19735R.M.Range & Y.T.Siu[8]# } q = n − 1 N β = 0  ∂̄– 0[9AU!^bJ q, |.;∂D ℄|o β = 0, 1974 5 W.Fischer o I.Lieb[16] Kb #!^ β 6= 0,|℄|.; ∂D o q = n − 1  ∂̄– 0[9AU^ 1986 5X I.Lieb& R.M.Range[17]  (=ZIW B.Fischer[18]). |	W Leray Sy厦门大学博硕士论文摘要库Stein 	KB q- Rs	 ∂̄- /Y8	?T 7Y^ λ  "OaMkZF! λ 2Æ6}X^K3SewW1 ≤ q ≤ n− 2 N.; ∂D ℄|* N  "`Jf b. Leray SyY^ λ ?v "}	FiF!m$ R.A.Airapetjan & G.M.Henkin[11]Eb;(}} Leray SyY^ λ 2 "u! λ 2Æ62t.Mk;EbAFt+;1j Leray SyY^ λ F)AD$Z+qxrTU^ Fantappie-Feynman O [11], ÆdÆ6 ZZ22; Henkin[19] Eb1) Q{AFY^ λ D$Z+ Leray Sy2) rTU^ Fantappie-Feynman O! λ Æ63) !Æ6(B U| C.Laurent-Thiebaut & J.Leiterer[10] (};[V	F7=t.9F;J#  Henkin 0)?D$ Leray Sy%rTXR.M.Range & Y.T.Siu[8] o W.Fischer & I. Lieb[16] U^Q{SyN# x)AsKJKt	F Leray Sy9BD$7\	! λB ÆdÆ6 ?Z2|Lf R.A.Airapetjan & G.M.Henkin[11] U^ Fantappie-Feynman Oj394UZF	FÆ6}Un%  Cn uLC q- Su (n, r)  ∂̄- 0[9AU'g+OT C.Laurent-Thiebauto J.Leiterer[10] 1rT Her-mitian }oSx [13] FLC~L! Stein LC q- Su ∂̄-0[9B AUA'{<x  Stein u<Mo<`MozaÆ'KF'Nm ZAjoi#	`NK_w"Æ6O∂̄- 0[oAUK:#'{ D ⊂⊂ M  Stein uLC q- S (UD̄, ρ1, · · · , ρN) C2 5$KbY^ λ 2 " Leray 4"rT Hermitian }oSx[13], Q{ Stein Y^ (r, s) ℄6x?2}tI*Æ6ln%  Stein uLC q- S D uOOo ∂̄- 0[9 [14].qx Stein urT Hermitian }oSx [13] FLC~厦门大学博硕士论文摘要库Stein 	KB q- Rs	 ∂̄- /Y8	?T 8LNB Os o m 6>Kb Æ66> H AU\wvrT R.M.Range & Y.T.Siu[8] 0)Kb ∂̄- 0[9AU厦门大学博硕士论文摘要库Stein 	KB q- Rs	 ∂̄- /Y8	?T 9py Stein .nms}T(x	Aok<x  Stein ZYKo'Nm_w"moUK:#§1.1 Stein ,lr| 1.1.1[4,5] { X A< n a< ϑ = ϑ(X) _ X uWih* X T_ Stein j=FtqFK*(i) X WiS! X $bA? K,K̂ϑ ={z ∈ X : |f(z)| ≤ supK|f |, ∀f ∈ ϑ(X)}= X $?(ii) X $Wih*Z6k X u!^bJ z, w ∈ X, z 6= w, qxf ∈ ϑ(X), Æ f(z) 6= f(w);(iii) X uWih*ZKb X LCM5!^bJ z ∈ X, qxf1, · · · , fn ∈ O(X), (f1, · · · , fn)  z AFeLCM5 H.Grauert[1958] ZAF}[mj X A<PZK$moQ6h*- X  Stein |;TK* (i) o (ii) JZF# Stein ZAK$moQ6h*MkX Grauert mZx SteinK$K* (ii) $`r| 1.1.2[4,5] <Moo<`MoD-*{ X AF< n a< {(Uj, hj)}  X WiM5T{Uj ⊂⊂ X.  Gij(z) := Jhi◦h−1j (z), z ∈ Ui ∩Uj , 	o Jhi◦h−1j (z)  hi ◦ h−1j x z Jacobi M-x Ui ∩Uj ∩Uk Z GijGjk = Gik. Xfh* Gij K XuWi}oT T (X) 8TK X u<MoXfh* (Gtij)−1 KX uWi}oT T ∗(X) 8TK X u<`Mo	o (Gij)t  Gij7 T (X) o T ∗(X) x z ∈ X zaT Tz(X) o T ∗z (X) 8 T (X)厦门大学博硕士论文摘要库Stein +kW q- VbkBj ∂̄- v^jv  10o T ∗(X) Y^QR X ×X −→ X, (z, ζ) −→ z e6:_ T̃ (X ×X) oT̃ ∗(X ×X).T (X) Wi4"6:_ S(z, ζ), ZS(z, ζ) : X ×X −→ T̃ (X ×X),-} X AGLCZU:A {Uj}, Æ!A j, ZAGWiM5hj : Uj −→ Cn FAWi?+~ ψj : T (X)|Uj −→ Uj×Cn. Dm' {χj} _An'^ {Uj} C∞{d69-A T (X)V S(z, ζ)xr D ⊆ XuZFoA}G {S(j)} ÆOD$}G {S(j)} Xx hj(Uj ∩D) ⊆ Cnu S(j)r Wih*} S(j) = (S(j)1 , · · · , S(j)n ) 9QVK S(z, ζ) -*_∥∥∥S(z, ζ)∥∥∥ :=∑jχj(z)n∑r=1∥∥S(j)r (hj(z))∥∥ , z ∈ D.D$ ∥∥∥S(j)r (hj(z))∥∥∥ r*_ S(j)r (hj(z)) }8Q§1.2 R &t"'NmZI)g~ [8] $Nm 4.2.4.' 1.2.1[4] { X AF< n a Stein  T (X)  X u<Mov#{ X AFMv Stein u!?U-qxAFWiSyS : X ×X −→ T (X) o X ×X uWih* ϕ FFtK*(i) !^bJ z, ζ ∈ X, S(z, ζ) ∈ Tz(X)( S(z, ζ) o T (X) Y^SyX ×X ∋ (z, ζ) −→ z ∈ X eu4").(ii) !bJX z ∈ X, S(z, z) = 0,n X  Tz(X)Sy S(z, ζ)x ζ = zeu,Wi(iii) !bJ z ∈ X, ϕ(z, z) = 1.(iv) j FS X S  V X×Xϑ1 9o>K- ϕ ∈ FS((X × X) \{(z, z) : z ∈ X}).厦门大学博硕士论文摘要库Stein +kW q- VbkBj ∂̄- v^jv  11(v) qxAF* ℵ ≥ 0 Æ T (X) $!^bJ-* ‖ · ‖, h* ϕℵ‖S‖−2x (X ×X) \ {(z, z) : z ∈ X}  C2  Nm$#{ X _AMv Stein !?U>ZF?;Nm8Vu§1.3 PI' v = (v1, · · · , vn) o u = (u1, · · · , un) _< -  X u< C(1)– h*K< v, u >= v1u1 + · · ·+ vnun,ω(u) = du1 ∧ · · · ∧ dun,ω′(v) =n∑j=1(−1)j−1vj∧s 6=jdvs,Ω(v, u) =(n− 1)!(2πi)nω′(v) ∧ ω(u)< v, u >n.j ζ 8 X u2}%h* vj o uj  Bh^D;2}~_ ωζ,ω′ζ o Ωζ . j vj o uj $u2}?AF~	u2};5bFtk# {(Uj , hj)}  X WiM5TÆ!9Z j, Uj ⊂⊂X. j D  X $U~ T (X) o T ∗(X) x D u_ T (D)o T ∗(D). LNK 1.1.2, }xXWi?+~ ψj : T (Uj) −→ Uj × Cn oψ∗j : T∗(Uj) −→ Uj × Cn Æ(z,(Gij(z))ζ)= ψi◦ψ−1j (z, ζ),(z,((Gtij)−1(z))ζ)= ψ∗i ◦(ψ∗j )−1(z, ζ),z ∈ Ui ∩ Uj , ζ ∈ Cn.j z ∈ Uj o a ∈ Tz(X)(a ∈ T ∗z (X)), -PZ ψj(a) = (z, aj)(ψ∗j (a) =(z, aj)) } aj ∈ Cn T_ a Y^ {(Uj, hj)} 8j z ∈ Ui ∩ Uj ,a ∈ Tz(X), b ∈ T ∗z (X) N ai, aj, bi, bj 6:_ a, b Y^ (Ui, hi) o (Uj , hj) 8-Zai = Gij(z)aj , bi = (Gtij)−1(z)bj .厦门大学博硕士论文摘要库Degree papers are in the “Xiamen University Electronic Theses and Dissertations Database”. Fulltexts are available in the following ways: 1. If your library is a CALIS member libraries, please log on http://etd.calis.edu.cn/ and submitrequests online, or consult the interlibrary loan department in your library. 2. For users of non-CALIS member libraries, please mail to etd@xmu.edu.cn for delivery details.厦门大学博硕士论文摘要库

Uniform Estimates of Solutions of Equations on Local q-Convex Wedges in Stein Manifolds

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Uniform Estimates of Solutions of Equations on Local q-Convex Wedges in Stein Manifolds

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