Extrinsic Geometry of Convex Surfaces
Author: Alekseĭ Vasilʹevich Pogorelov
Publisher: American Mathematical Soc.
Published: 1973
Total Pages: 680
ISBN-13: 9780821886618
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Extrinsic Geometry of Convex Surfaces
Author: A. V. Pogorelov
Publisher:
Published: 1973
Total Pages: 669
ISBN-13: 9780706512618
DOWNLOAD EBOOKConvex Surfaces
Author: Herbert Busemann
Publisher: Courier Corporation
Published: 2013-11-07
Total Pages: 210
ISBN-13: 0486154998
DOWNLOAD EBOOKThis exploration of convex surfaces focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. It also examines intrinsic geometry and the realization of intrinsic metrics. 1958 edition.
Extrinsic Geometry of Convex Surfaces
Author: Alekseĭ Vasilʹevich Pogorelov
Publisher:
Published: 1973
Total Pages: 677
ISBN-13: 9781470444501
DOWNLOAD EBOOKDifferential Geometry of Curves and Surfaces
Author: Victor Andreevich Toponogov
Publisher: Springer Science & Business Media
Published: 2006-09-10
Total Pages: 215
ISBN-13: 0817644024
DOWNLOAD EBOOKCentral topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels
Geometry III
Author: Yu.D. Burago
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 263
ISBN-13: 3662027518
DOWNLOAD EBOOKA volume devoted to the extremely clear and intrinsically beautiful theory of two-dimensional surfaces in Euclidean spaces. The main focus is on the connection between the theory of embedded surfaces and two-dimensional Riemannian geometry, and the influence of properties of intrinsic metrics on the geometry of surfaces.
Curves and Surfaces
Author: Sebastián Montiel
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 395
ISBN-13: 0821847635
DOWNLOAD EBOOKOffers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.
Handbook of Convex Geometry
Author: Bozzano G Luisa
Publisher: Elsevier
Published: 2014-06-28
Total Pages: 803
ISBN-13: 0080934390
DOWNLOAD EBOOKHandbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.
Geometry IV
Author: Yurĭi Grigorevǐc Reshetnyak
Publisher: Springer Science & Business Media
Published: 1993-10-14
Total Pages: 274
ISBN-13: 9783540547013
DOWNLOAD EBOOKThis book contains two surveys on modern research into non-regular Riemannian geometry, carried out mostly by Russian mathematicians. Coverage examines two-dimensional Riemannian manifolds of bounded curvature and metric spaces whose curvature lies between two given constants. This book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry.
Lectures on Classical Differential Geometry
Author: Dirk J. Struik
Publisher: Courier Corporation
Published: 2012-04-26
Total Pages: 254
ISBN-13: 0486138186
DOWNLOAD EBOOKElementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
