This volume of 15 contributed papers is a tribute to Professor Guangchang Dong on the occasion of his 80th birthday. These are survey or expository papers on recent developments in the theory of partial differential equations and their applications in geometry, physics, finance, and other areas, which also reflect Professor Dong's main research interests in his career. This volume is intended for researchers and graduate students to catch up recent developments in these areas.

The launch of this Advanced Lectures in Mathematics series is aimed at keeping mathematicians informed of the latest developments in mathematics, as well as to aid in the learning of new mathematical topics by students all over the world. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. This series emphasizes the history and sources of motivation for the topics under discussion, and also gives an overview of the current status of research in each particular field. These volumes are the first source to which people will turn in order to learn new subjects and to discover the latest results of many cutting-edge fields in mathematics.

Preface

Baojun Bian and Yang Wang: Viscosity Solutions of Bellman Equations

  Arising in Pricing Passport Options

Kai-Seng Chou and Shi-Zhong Du: On Global Partial Regularity for

  Borderline Solutions of Semilinear Parabolic Problems

Bo Guan: The Dirichlet Problem for Complex Monge-Ampere

  Equations and Applications

Yongsheng Han and Guozhen Lu : Some Recent Works on Multiparameter

  Hardy Space Theory and Discrete Littlewood-Paley Analysis

Min-Chun Hong: Some Analytic Aspects of Liquid Crystal

  Configurations

De-Xing Kong: Extremal Sub-manifolds in Minkowski Space-time

Jun Ling and Zhiqin Lu: Bounds of Eigenvalues on Riemannian

  Manifolds

Yue Liu : Wave Breaking Phenomena and Stability of Peakons for the

  Degasperis-Procesi Equation

Xi-Nan Ma and Qianzhong Ou : The Convexity of Level Sets for

  Solutions to Partial Differential Equations

Xing-Bin Pan : Nucleation of Instability of Meissner State of

  Superconductors and Related Mathematical Problems

Yi-Bing Shen: Calculus of Some Geometric Variations in

  Finsler Geometry

Weimin Sheng and Xu-Jia Wang: Regularity and Singularity in

  the Mean Curvature Flow

Longjun Shen and Guixia Lv : Study of Finite Point Method

Jingxue Yin, Peidon9 Lei and Chunpeng Wang: Nonlinear Diffusion

  Equations with Different Kind of Degeneracy

Xiaohua Zhu: Canonical Metrics on Toric Manifolds

List of publications by Guangchang Dong