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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Kazdan-Warner equations on compact Riemann surfaces
紧黎曼曲面 卡兹丹-华纳方程 数学
2023/4/28
In this talk, we shall review firstly the study history of Kazdan-Warner equations on compact Riemann surfaces, which was proposed by Kazdan and Warner on Annals of Math on 1974. Then we shall show th...
ENERGY OF TWISTED HARMONIC MAPS OF RIEMANN SURFACES
Riemann surface fundamental group flat bundle harmonic map energy Teichmuller space convex cocompact hyperbolic manifold
2015/12/17
The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function E ρ on Teichm¨uller space TS which is a qualitative invariant of the ...
We produce for each natural number n 3 two 1–parameter fam-ilies of Riemann surfaces admitting automorphism groups with two cyclic sub-groups H1 and H2 of orden 2n, that are conjugate in the group o...
We show that for any fixed point P0 on a Riemann surface the distinct realizations of cocycles in H1(,O) correspond to the natural appearances of the standard Heisenberg vertex operator algebra (P0...
Addendum to "Energies of zeros of random sections on Riemann surfaces" [arXiv:0705.2000]. Indiana Univ. Math. J. 57 (2008), no. 4, 1753-1780
Energies of zeros of random sections Riemann surfaces
2010/12/9
The purpose of this note is to resolve an apparent discrepancy between the calculations
in the article [ABS] of Armentano- Beltran-Shub (henceforth ABS) and that in Qi Zhong’s
article [Zh] of the as...
The topology of balls and Gromov hyperbolicity of Riemann surfaces
Topology of balls uniformly separated sets Riemann surfaces Gromov hyperbolicity
2010/12/9
For each k > 0 we find an explicit function fk such that the topology of S inside the ball
BS(p, r) is ‘bounded’ by fk(r) for every complete Riemannian surface (compact or noncompact) S with K W...
Balanced metrics and chow stability of projective bundles over Riemann surfaces
Balanced metrics chow stability of projective bundles Riemann surfaces
2010/12/15
In 1980, I. Morrison proved that slope stability of a vector bundle of rank 2 over a compact Riemann surface implies Chow stability of the projectivization of the bundle with respect to certain polari...
Recent Development on the Geometry of the Teichuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds
Geometry of the Teichuller Moduli Spaces Riemann Surfaces Polarized Calabi-Yau Manifolds
2018/4/19
The moduli spaceMg,k of Riemann surfaces of genus g with k punctures plays an important role in many area of mathematics and theoretical physics.In this article we first survey some of our recent work...
In this paper we briefly survey our recent results about the Mumford goodness of several canonical metrics on the moduli spaces of Riemann surfaces. We will also prove the dual Nakano negativity of th...
GEOMETRIC ASPECTS OF THE MODULI SPACE OF RIEMANN SURFACES
Introduction The Topological Aspects Moduli Space Background of the Teichm¨uller Theory
2018/4/20
The study of moduli space and Teichm¨uller space has a long history. These two spaces lie in the intersections of the researches in many areas of mathematics and physics. Many deep results have been o...