14,457 research outputs found
Progress on Hardy-type Inequalities
This paper surveys some of our recent progress on Hardy-type inequa\-lities
which consist of a well-known topic in Harmonic Analysis. In the first section,
we recall the original probabilistic motivation dealing with the stability
speed in terms of the -theory. A crucial application of a result by
Fukushima and Uemura (2003) is included. In the second section, the non-linear
case (a general Hardy-type inequality) is handled with a direct and analytic
proof. In the last section, it is illustrated that the basic estimates
presented in the first two sections can still be improved considerably.Comment: 13 pages, 5 figures, Festschrift Masatoshi Fukushima: In Honor of
Masatoshi Fukushima's Sanju. World Scientific, 201
A Nonabelian Tensor Multiplet Theory in 6D
We construct a general nonabelian (1,0) tensor multiplet theory in six
dimensions. The gauge field of this (1,0) theory is non-dynamical, and the
theory contains a continuous parameter . When , the (1,0) theory
possesses an extra discrete symmetry enhancing the supersymmetry to (2,0), and
the theory turns out to be identical to the (2,0) theory of Lambert and
Papageorgakis (LP). Upon dimension reduction, we obtain a general
supersymmetric Yang-Mills theory in five dimensions. The applications of the
theories to D4 and M5-branes are briefly discussed.Comment: 18 pages, published in JHEP. minor changes, references adde
General estimate of the first eigenvalue on manifolds
Ten sharp lower estimates of the first non-trivial eigenvalue of Laplacian on
compact Riemannian manifolds are reviewed and compared. An improved variational
formula, a general common estimate, and a new sharp one are added. The best
lower estimates are now updated. The new estimates provide a global picture of
what one can expect by our approach.Comment: 19 page
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