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This book focuses on Hamilton's Ricci flow, beginning with a
detailed discussion of the required aspects of differential
geometry, progressing through existence and regularity theory,
compactness theorems for Riemannian manifolds, and Perelman's
noncollapsing results, and culminating in a detailed analysis of
the evolution of curvature, where recent breakthroughs of Bohm and
Wilking and Brendle and Schoen have led to a proof of the
differentiable 1/4-pinching sphere theorem.
Extrinsic geometric flows are characterized by a submanifold
evolving in an ambient space with velocity determined by its
extrinsic curvature. The goal of this book is to give an extensive
introduction to a few of the most prominent extrinsic flows,
namely, the curve shortening flow, the mean curvature flow, the
Gauss curvature flow, the inverse-mean curvature flow, and fully
nonlinear flows of mean curvature and inverse-mean curvature type.
The authors highlight techniques and behaviors that frequently
arise in the study of these (and other) flows. To illustrate the
broad applicability of the techniques developed, they also consider
general classes of fully nonlinear curvature flows. The book is
written at the level of a graduate student who has had a basic
course in differential geometry and has some familiarity with
partial differential equations. It is intended also to be useful as
a reference for specialists. In general, the authors provide
detailed proofs, although for some more specialized results they
may only present the main ideas; in such cases, they provide
references for complete proofs. A brief survey of additional
topics, with extensive references, can be found in the notes and
commentary at the end of each chapter.
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The Device (DVD)
Russell Hodgkinson, Kate Alden, Gabriel Congdon, David S. Hogan, Angela Dimarco, …
1
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R55
Discovery Miles 550
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Out of stock
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Jeremy Berg writes, directs and produces this horror starring
Angela DiMarco and Kate Alden. When sisters Abby and Rebecca
(DiMarco and Alden) return home after a long time away, they decide
to revist a place from their childhood. As they walk through the
woods to a beautiful lake they notice a small, spherical object
lying on the ground. Tentatively, the sisters take the item home
but when terrifying things begin to happen to them they start to
regret ever having found it...
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