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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 ...
A computation of the constant appearing in the spin-1 bosonization formulais given. This constant relates Faltings’ delta invariant to the zeta-regularized determinant of the Laplace operator with res...
We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary...
In this paper, by using the Kuranishi coordinates on the Teichm¨uller spaceand the explicit deformation formula of holomorphic one-forms on Riemann surface, we give an explicit expression of the peri...
Abstract: In the present paper we solve the following different but interrelated problems: (a) the moment problem on Riemann surfaces, (b) the vanishing problem of polynomial Abelian integrals of dime...
Abstract: The geometric notion of ellipticity for complex manifolds was introduced by Gromov in his seminal 1989 paper on the Oka principle, and is a sufficient condition for a manifold to be Oka. In ...
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...
We consider simply connected log-Riemann surfaces with a finite number of ramification points. We prove that these surfaces are biholomorphic to C with uniformizations given by entire functions of th...
We define the notion of log-Riemann surfaces and Caratheodory convergence of log-Riemann surfaces. We prove a convergence theorem for uniformizations of simply connected log-Riemann surfaces convergin...
n-point functions of holomorphic fields in rational conformal field theories can be calculated by methods from complex analysis. We establish explicit formulas for the 2-point functions of the Viraso...
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...
We prove the existence of Alexandrov embedded closed magnetic geodesics on closed hyperbolic surfaces. Closed magnetic geodesics correspond to closed curves with prescribed geodesic curvature.

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