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Comparison Geometry
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Karsten Grove (Editor), Peter Petersen (Editor)
This book documents the focus on a branch of Riemannian geometry called Comparison Geometry. The simple idea of comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has seen a tremendous evolution of late. This volume is an up-to-date reflection of the recent development regarding spaces with ...
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Geometry of Surfaces
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John Stillwell
This text intends to provide the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. The geometry of surfaces is an ideal starting point for students learning geometry for the following ...
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Constant Mean Curvature Surfaces, Harmonic Maps, and Integrable Systems
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Frederic Helein
This book intends to give an introduction to harmonic maps between a surface and a symmetric manifold and constant mean curvature surfaces as completely integrable systems. The presentation is accessible to undergraduate and graduate students in mathematics but will also be useful to researchers. It is among the first textbooks about integrable ...
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Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature
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Tatiana G Vozmischeva
This book combines a most interesting area of study, celestial mechanics, with modern geometrical methods in physics. According to recently developed views and research, one of the basic qualitative characteristics of an integrable Hamiltonian system is a structure of the Liouville foliation. A number of interesting results have been obtained. In ...
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Curvature and Characteristic Classes
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J L DuPont
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Curvature and Homology
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Samuel I Goldberg
Thorough treatment of specialized branch of differential geometry. Covers Riemannian manifolds, topology of differentiable manifolds, compact Lie groups, other topics. Exercises.
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Surfaces with Constant Mean Curvature
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by
K Kenmotsu
The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. There is a rich and well-known theory of minimal surfaces. A surface whose mean ...
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The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds
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by
Peter B Gilkey
Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and ...
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Curvature Cosmology: A Model for a Static, Stable Universe
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David F Crawford
Curvature Cosmology proposes a new cosmological model very different from, and more elegant than, the Big-Bang Theory. Curvature Cosmology is based on two major hypotheses that Hubble redshift is due to an interaction of photons with curved spacetime and that there is a pressure that acts to stabilise expansion and provides a static stable ...
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Geometry II: Spaces of Constant Curvature
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E B Vinberg (Editor)
This book contains a systematic and comprehensive exposition of Lobachevskian geometry and the theory of discrete groups of motions in Euclidean space and Lobachevsky space. The authors give a very clear account of their subject describing it from the viewpoints of elementary geometry, Riemannian goemetry and group theory. The result is a book ...
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Appearance and Essence: Refinements of Classical Architecture--Curvature
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Lothar Haselberger (Editor)
The proceedings of the second Williams Symposium explore the phenomenon of curvature, together with other such "secrets" of classical refinement. Debated ever since the Renaissance, these stunning architectural subtleties are treated here for the first time in a combined effort of international experts. Ranging from painstaking new technical ...
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Radiative Transfer in Curved Media
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K. K. Sen (Editor), S. J. Wilson (Editor)
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The language of shape the role of curvature in condensed matter physics, chemistry and biology
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by
Hyde
This book develops the thesis that structure and function in a variety of condensed systems - from the atomic assemblies in inorganic frameworks and organic molecules, through molecular self-assemblies to proteins - can be unified when curvature and surface geometry are taken together with molecular shape and forces. An astonishing variety of ...
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Geometry
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E. B. Vinberg
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Curvature & Betti Numbers
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by
Kentareo Yano, S Bochner
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Lectures on Mean Curvature Flows
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by
XI-Ping Zhu
'Mean curvature flow' is a term that is used to describe the evolution of a hyper surface whose normal velocity is given by the mean curvature. In the simplest case of a convex closed curve on the plane, the properties of the mean curvature flow are described by Gage-Hamilton's theorem. This theorem states that under the mean curvature flow, the ...
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Curvature and Homology: Enlarged Edition
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by
Samuel I Goldberg
Revised edition examines topology of differentiable manifolds; curvature, homology of Riemannian manifolds; compact Lie groups; complex manifolds; curvature, homology of Kaehler manifolds. New Preface. Four new appendixes.
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Elliptic Regularization and Partial Regularity for Motion by Mean Curvature
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Tom Ilmanen
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Prescribing the Curvature of a Riemannian Manifold
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by
Jerry L. Kazdan, Conference Board of the Mathematical Sci
These notes were the basis for a series of ten lectures given in January 1984 at Polytechnic Institute of New York under the sponsorship of the Conference Board of the Mathematical Sciences and the National Science Foundation. The lectures were aimed at mathematicians who knew either some differential geometry or partial differential equations, ...
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The Motion of a Surface by Its Mean Curvature
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Kenneth A. Brakke
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Motion by Mean Curvature and Related Topics: Proceedings of the International Conference Held at Trento, July 20-24, 1992
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Giuseppe Buttazzo
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Total Mean Curvature and Submanifolds of Finite Type
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Chen
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Exploring curvature
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by
James Casey
This introductory text is exploratory in nature, and is intended as a bridge between Euclid's geometry and the modern geometry of curved spaces. It is organized around a collection of simple experiments which the reader can perform at home or in a classroom setting. Methods for physically exploring the intrinsic geometry of commonplace curved ...
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Total Mean Curvature and Submanifolds of
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Bang-Yen Chen
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Curvature and Variational Modeling in Physics and Biophysics
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by
Oscar J Garay (Editor), Eduardo Garcia-Rio (Editor), Ramon Vasquez-Lorenzo (Editor)
The School was mainly addressed to young researchers coming from different disciplines with a common interest in variational problems defined by curvature energy functionals. Curves and surfaces obtained as critical points of these functionals are investigated from a theoretical and numerical point of view. Applications are shown in Geometry, ...
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