Self-similar Solutions to the Mean Curvature Flow Based on the Lawson-Osserman Cone
Title | Self-similar Solutions to the Mean Curvature Flow Based on the Lawson-Osserman Cone PDF eBook |
Author | 李宸寬 |
Publisher | |
Pages | 0 |
Release | 2022 |
Genre | |
ISBN |
Numerical Computation of Self-similar Solutions for Mean Curvature Flow
Title | Numerical Computation of Self-similar Solutions for Mean Curvature Flow PDF eBook |
Author | David L. Chopp |
Publisher | |
Pages | 18 |
Release | 1993 |
Genre | |
ISBN |
Self-similar Expanding Solutions for a Multiphase Mean Curvature Flow
Title | Self-similar Expanding Solutions for a Multiphase Mean Curvature Flow PDF eBook |
Author | 廖偉宏 |
Publisher | |
Pages | |
Release | 2019 |
Genre | |
ISBN |
Hamilton’s Ricci Flow
Title | Hamilton’s Ricci Flow PDF eBook |
Author | Bennett Chow |
Publisher | American Mathematical Society, Science Press |
Pages | 648 |
Release | 2023-07-13 |
Genre | Mathematics |
ISBN | 1470473690 |
Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.
Global Theory of Minimal Surfaces
Title | Global Theory of Minimal Surfaces PDF eBook |
Author | Clay Mathematics Institute. Summer School |
Publisher | OECD Publishing |
Pages | 820 |
Release | 2005 |
Genre | Mathematics |
ISBN | 9780821835876 |
In the Summer of 2001, the Mathematical Sciences Research Institute (MSRI) hosted the Clay Mathematics Institute Summer School on the Global Theory of Minimal Surfaces. During that time, MSRI became the world center for the study of minimal surfaces: 150 mathematicians--undergraduates, post-doctoral students, young researchers, and world experts--participated in the most extensive meeting ever held on the subject in its 250-year history. The unusual nature of the meeting made it possible to put together this collection of expository lectures and specialized reports, giving a panoramic view of a vital subject presented by leading researchers in the field. The subjects covered include minimal and constant-mean-curvature submanifolds, geometric measure theory and the double-bubble conjecture, Lagrangian geometry, numerical simulation of geometric phenomena, applications of mean curvature to general relativity and Riemannian geometry, the isoperimetric problem, the geometry of fully nonlinear elliptic equations and applications to the topology of three-dimensional manifolds. The wide variety of topics covered make this volume suitable for graduate students and researchers interested in differential geometry. Information for our distributors: Titles in this series are published by the AMS for the Clay Mathematics Institute (Cambridge, MA).
The Shape of Inner Space
Title | The Shape of Inner Space PDF eBook |
Author | Shing-Tung Yau |
Publisher | Il Saggiatore |
Pages | 398 |
Release | 2010-09-07 |
Genre | Mathematics |
ISBN | 0465020232 |
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
Spectral Geometry
Title | Spectral Geometry PDF eBook |
Author | Pierre H. Berard |
Publisher | Springer |
Pages | 284 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540409580 |