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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...
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...
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...
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...
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...
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...
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...

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