The Chern-Ricci flow on complex surfaces

The Chern-Ricci flow is an evolution equation of Hermitian metrics by their Chern-Ricci form, first introduced by Gill. Building on our previous work, we investigate this flow on complex surfaces. We establish new estimates in the case of finite time non-collapsing, anologous to some known results for the Kahler-Ricci flow. This provides evidence that the Chern-Ricci flow carries out blow-downs of exceptional curves on non-minimal surfaces. We also describe explicit solutions to the Chern-Ricci flow for various non-Kahler surfaces. On Hopf surfaces and Inoue surfaces these solutions, appropriately normalized, collapse to a circle in the sense of Gromov-Hausdorff. For non-Kahler properly elliptic surfaces, our explicit solutions collapse to a Riemann surface. Finally, we define a Mabuchi energy functional for complex surfaces with vanishing first Bott-Chern class and show that it decreases along the Chern-Ricci flow.Comment: 45 page

Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains

This paper lays down a foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theory based on the representation theory of SL(2,R) group. We describe here geometries of corresponding domains. The principal role is played by Clifford algebras of matching types. Keywords: analytic function theory, semisimple groups, elliptic, parabolic, hyperbolic, Clifford algebrasComment: 14 pages, AMS-LaTeX, 31 PS graphcs in 7 Figures; v2--the missing PS file is included now; v3 minor corrections, reference added; v4 numerous misprints correcte

Cyclic cohomology for graded C∗,rC^{*,r}-algebras and its pairings with van Daele KK-theory

We consider cycles for graded $C^{*,r}$-algebras (Real $C^{*}$-algebras) which are compatible with the $*$-structure and the real structure. Their characters are cyclic cocycles. We define a Connes type pairing between such characters and elements of the van Daele $K$-groups of the $C^{*,r}$-algebra and its real subalgebra. This pairing vanishes on elements of finite order. We define a second type of pairing between characters and $K$-group elements which is derived from a unital inclusion of $C^{*}$-algebras. It is potentially non-trivial on elements of order two and torsion valued. Such torsion valued pairings yield topological invariants for insulators. The two-dimensional Kane-Mele and the three-dimensional Fu-Kane-Mele strong invariant are special cases of torsion valued pairings. We compute the pairings for a simple class of periodic models and establish structural results for two dimensional aperiodic models with odd time reversal invariance.Comment: 57 page

Search for young stars among ROSAT All-Sky Survey X-ray sources in and around the R CrA dark cloud

We present the ROSAT All-Sky Survey data in a 126 deg^2 area in and around the CrA star forming region. With low-resolution spectroscopy of unidentified ROSAT sources we could find 19 new pre-main sequence stars, two of which are classical T Tauri stars, the others being weak-lined. The spectral types of these new T Tauri stars range from F7 to M6. The two new classical T Tauri stars are located towards two small cloud-lets outside of the main CrA cloud. They appear to be ~10 Myrs old, by comparing their location in the H-R diagram with isochrones for an assumed distance of 130 pc, the distance of the main CrA dark cloud. The new off-cloud weak-line T Tauri stars may have formed in similar cloud-lets, which have dispersed recently. High-resolution spectra of our new T Tauri stars show that they have significantly more lithium absorption than zero-age main-sequence stars of the same spectral type, so that they are indeed young. From those spectra we also obtained rotational and radial velocities. For some stars we found the proper motion in published catalogs. The direction and velocity of the 3D space motion - south relative to the galatic plane - of the CrA T Tauri stars is consistent with the dark cloud being formed originally by a high-velocity cloud impact onto the galactic plane, which triggered the star formation in CrA. We also present VRIJHK photometry for most of the new T Tauri stars to derive their luminosities, ages, and masses.Comment: A&A Suppl. in pres

Representation Theory of The W1+∞W_{1+\infty} Algebra

We review the recent development in the representation theory of the $W_{1+\infty}$ algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (Super) Matrix Generalization, Structure of subalgebras such as $W_\infty$ algebra, Determinant formula, Character formula. (Invited talk at ``Quantum Field Theory, Integrable Models and Beyond", YITP, 14-17 February 1994. To appear in Progress of Theoretical Physics Proceedings Supplement.)Comment: 36 pages, LaTeX, RIMS-990, YITP/K-1087, YITP/U-94-25, SULDP-1994-

Moving and oblique observations of beams and plates

We study the observability of the one-dimensional Schr{\"o}dinger equation and of the beam and plate equations by moving or oblique observations. Applying different versions and adaptations of Ingham's theorem on nonharmonic Fourier series, we obtain various observability and non-observability theorems. Several open problems are also formulated at the end of the paper