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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
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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
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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 ...
Precise Constants in Bosonization Formulas on Riemann Surfaces. I
Bosonization Formulas Riemann Surfaces
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2015/12/17
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...
GLUING FORMULAS FOR DETERMINANTS OF DOLBEAULT LAPLACIANS ON RIEMANN SURFACES
Determinants of Laplace operators Riemann surfaces bosonization formulas
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2015/12/17
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...
HIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES
HIGGS BUNDLES LOCAL SYSTEMS RIEMANN SURFACES
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2015/12/17
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...
Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces
Higgs Bundles Fundamental Groups
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2015/9/29
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...
ENERGY OF TWISTED HARMONIC MAPS OF RIEMANN SURFACES
RIEMANN SURFACES HARMONIC MAPS
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2015/9/29
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...
NEW PROOFS OF THE TORELLI THEOREMS FOR RIEMANN SURFACES
NEW PROOFS THE TORELLI THEOREMS RIEMANN SURFACES
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2018/4/19
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...
Moments on Riemann surfaces and hyperelliptic Abelian integrals
Moments Riemann surfaces hyperelliptic Abelian integrals Dynamical Systems
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2011/9/9
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...
Acyclic embeddings of open Riemann surfaces into new examples of elliptic manifolds
Holomorphic embedding Riemann surface Oka manifold Stein manifold elliptic manifold affine manifold
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2011/8/22
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 ...
Equivalence of Group Actions on Riemann Surfaces
Equivalence of Group Riemann Surfaces
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2011/2/24
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...
Riemann Surfaces and Vertex Operator Algebras
Riemann Surfaces Vertex Operator Algebras
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2011/1/21
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...
Uniformization of simply connected finite type log-Riemann surfaces
simply connected finite type log-Riemann surfaces
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2010/11/9
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...
Caratheodory convergence of log-Riemann surfaces and Euler's formula
Caratheodory convergence log-Riemann surfaces Euler's formula
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2010/11/9
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...
CFTs on Riemann Surfaces of genus $g\geq 1$
CFTs Riemann Surfaces
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2010/11/12
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...