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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...
These notes are based on lectures given at the Third International School on Geometry and Physics at the Centre de Recerca Matem`atica in Barcelona, March 26–30, 2012. The aim ofthe School’s four lect...
Goldman gratefully acknowledges partial support by NSF grants DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research Award from the General Research Board of the University of Maryland in Fa...
The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function Eρ on Teichm¨uller space TS which is a qualitative invariant...
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...

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