Variational Principles for Discrete Surfaces

Series: Advanced Lectures in Mathematics

Feng Luo
Rutgers University

Xianfeng David Gu
SUNY at Stony Brook

Junfei Dai
Zhejiang University

Abstract

This book intends to lead to some of the current topics of research in the geometry of polyhedral surfaces with applications to computer graphics. The main feature of the book is a systematic introduction to geometry of polyhedral surfaces based on the variational principle. The authors focus on using analytic methods in the study of some of the fundamental results and problems on polyhedral geometry, e.g., the Cauchy rigidity theorem, Thurston's circle packing theorem, rigidity of circle packing theorem and Colin de Verdiere's variational principle. With the vast development of the mathematics subject of polyhedral geometry, the present book is the first complete treatment of the subject.