An Introduction To The Analysis Of Paths On A Riemannian Manifold
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An Introduction to the Analysis of Paths on a Riemannian Manifold
Author: Daniel W. Stroock
language: en
Publisher: American Mathematical Soc.
Release Date: 2000
Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.
The Laplacian on a Riemannian Manifold
Author: Steven Rosenberg
language: en
Publisher: Cambridge University Press
Release Date: 1997-01-09
This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Analysis for Diffusion Processes on Riemannian Manifolds
Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.