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Extremal Riemann Surfaces
John R. QuinePeter Sarnak
其他書名
From the Proceedings of the AMS Special Session with Related Papers January 4-5, 1995, San Francisco, California
出版American Mathematical Soc., 1997
主題Mathematics / CalculusMathematics / Geometry / AlgebraicMathematics / Mathematical AnalysisMathematics / Topology
ISBN08218051429780821805145
URLhttp://books.google.com.hk/books?id=ws4aCAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋This volume is an outgrowth of the AMS Special Session on Extremal Riemann Surfaces held at the Joint Mathematics Meeting in San Francisco, January 1995. The book deals with a variety of extremal problems related to Riemann surfaces. Some papers deal with the identification of surfaces with longest systole (element of shortest nonzero) for the length spectrum and the Jacobian. Parallels are drawn to classical questions involving extremal lattices. Other papers deal with maximizing or minimizing functions defined by the spectrum such as the heat kernel, the zeta function, and the determinant of the Laplacian, some from the point of view of identifying an extremal logic. There are discussions of Hurwitz surfaces and surfaces with large cyclic groups of automorphisms. Also discussed are surfaces which are natural candidates for solving extremal problems such as triangular, modular, and arithmetic surfaces, and curves in various group theoretically defined curve families. Other allied topics are theta identities, quadratic periods of Abelian differentials, Teichm *uller disks, binary quadratic forms, and spectral asymptotics of degenerating hyperbolic three manifolds.