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 s…
This is a revised printing of one of the classic mathematics texts published in the last 25 years. This revised edition includes updated references and indexes and error corrections and will continue to serve as the standard text for students and professionals in the field. Diff…
Sasakian geometry
by Boyer, Charles P., Galicki, Krzysztof
fromOxford mathematical monographs
A multiple solution theory to the Plateau problem in a Riemannian manifold is established. In [italic capital]S[superscript italic]n, the existence of two solutions to this problem is obtained. The Morse-Tompkins-Shiffman Theorem is extended to the case when the ambient space ad…
This memoir investigates a method that generalizes the Chern-Federer kinematic formula to arbitrary homogeneous spaces with an invariant Riemannian metric, and leads to new formulas even in the case of submanifolds of Euclidean space.
This is a detailed paper concerning complete noncompact 2-dimensional Riemannian manifolds M with nonpositive Gaussian curvature.
In this paper we study the geodesics and ends of compact surfaces satisfying the "uniform visibility" axiom. We are primarily though not exclusively interested in finitely connected surfaces, which topologically are compact Riemann surfaces with a finite number of punctures.
This memoir develops the spectral theory of the Lax operators of nonlinear Schrödinger-like partial differential equations with periodic boundary conditions. Their special curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite ge…
We develop a link between the 'coarse' geometry of complete Riemannian manifolds and index theory for elliptic operators on such manifolds. We define and make use of a new cohomology theory that is sensitive only to this coarse geometry. The connection with index theory is made …