图书信息
图书目录
Recent Development in Geometry and Analysis(几何与分析中的最新进展)
本书汇集了微分几何、几何分析、微分方程等方面一些综述性文章或最新进展研究成果，特别有益于几何、分析专业的硕士生、博士生以及刚刚开始从事这些领域研究的数学工作者，对在相关领域工作的其他数学工作者也很有参考价值。
All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without permission.
作者：
东瑜昕 等
定价：
128.00元
出版时间：
2012-07-05
ISBN：
978-7-04-034825-5
物料号：
34825-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
几何分析
重点项目：
暂无
版面字数：
780.000千字
开本：
16开
全书页数：
522页
装帧形式：
精装
- Front Matter
- Minimal Volume and Simplicial Volume of Visibility n-manifolds and All 3-manifolds Jianguo Cao, Xiaoyang Chen
- 1 Introduction
- 2 Simplicial Volume and Bounded Cohomology
- 3 Visibility Manifolds and Gromov-hyperbolic Spaces
- 4 Gromov’s Simplicial Volume of Visibility n-manifolds and Compact 3-manifolds
- References
- Rigidity Theorems for Lagrangian Submanifolds of Complex Space Forms with Conformal Maslov Form Xiaoli Chao, Yuxin Dong
- 1 Introduction
- 2 Preliminaries
- 3 Rigidity Theorems for Lagrangian Submanifolds
- References
- Method of Moving Planes in Integral Forms and Regularity LiftingWenxiong Chen, Congming Li
- 1 Introduction
- 2 Illustration of MMP in Integral Forms
- 3 Various Applications of MMP in Integral Forms
- 4 Regularity Lifting by Contracting Operators
- 5 Regularity Lifting by Combinations of Contracting and Shrinking Operators
- References
- The Ricci Curvature in Finsler Geometry Xinyue Cheng
- 1 Definitions and Notations
- 2 Ricci Curvature of Randers Metrics
- 3 Volume Comparison in Finsler Geometry
- 4 The Role of the Ricci Curvature in Projective Geometry
- References
- Specific Non-K¨ahler Hermitian Metrics on Compact Complex Manifolds Jixiang Fu
- 1 Introduction
- 2 Balanced Metrics Under the Conifold Transition
- 3 The Supersymmetric Solutions
- 4 The Form-type Calabi-Yau Equation
- 5 The Generalized Gauduchon Metrics
- References
- On the _2-scalar Curvature and Its Applications Yuxin Ge, Guofang Wang
- 1 Introduction
- 2 _2-Yamabe Problem
- 3 A Quotient Equation
- 4 Ellipticity of a Quotient Equation and a 3-dimensional Sphere Theorem
- 5 A Rough Classification of Metrics of Positive Scalar Curvature
- 6 An Almost Schur Theorem
- References
- Isometric Embedding of Surfaces in R3 Qing Han
- 1 Introduction
- 2 Local Isometric Embedding of Surfaces
- 3 Global Isometric Embedding of Surfaces
- References
- The Lagrangian Mean Curvature Flow Along the K¨ahler-Ricci Flow Xiaoli Han, Jiayu Li
- 1 Introduction
- 2 Lagrangian Property Is Preserved
- References
- On Magnetohydrodynamics with Partial Magnetic Dissipation near Equilibrium Xianpeng Hu, Zhen Lei, Fang-Hua Lin
- 1 Introduction
- 2 Reformulation of the Ideal MHD
- 3 Global Existence
- 4 Acknowledgement
- References
- Hyperbolic Gradient Flow: Evolution of Graphs in Rn+1 De-Xing Kong, Kefeng Liu
- 1 Introduction
- 2 Hyperbolic Gradient Flow for Graphs in Rn+1
- 3 The Evolution of Convex Hypersurfaces in Rn+1
- 4 The Evolution of Plane Curves
- 5 Conclusions and Open Problems
- References
- The Moser-Trudinger and Adams Inequalities and Elliptic and Subelliptic Equations with Nonlinearity of Exponential Growth Nguyen Lam, Guozhen Lu
- 1 Introduction
- 2 The Moser-Trudinger Inequalities
- 3 Adams Type Inequalities on High Order Sobolev Spaces
- 4 N-Laplacian on Bounded Domains in RN
- 5 Polyharmonic Equations on Bounded Domains in R2m
- 6 N-Laplacian Equations with Critical Exponential Growth in RN
- 7 Existence of Solutions to Polyharmonic Equations with Critical Exponential Growth in the Whole Space
- 8 Subcritical Exponential Growth in Bounded Domains
- 9 Equations of Q-sub-Laplacian Type with Critical Growth on Bounded Domains
- 10 Equations of Q-sub-Laplacian Type with Critical Growth in Hn
- 11 Examples of Nonlinear Terms Without the Ambrosetti- Rabinowitz Condition
- 12 Sharp Moser-Trudinger Inequality on the Heisenberg Group at the Critical Case and Multiplicity of Solutions
- 13 A New Approach to Sharp Adams Inequalities for Arbitrary Integers and Less Restrictive Norms
- References
- Navigation Problem and Randers Metrics Meng Li, Xiaohuan Mo, Ni Yu
- 1 Historical Remarks and Definitions
- 2 Navigation Problem
- 3 Flag Curvature Decreasing Property of Navigation Problem
- 4 New Finsler Metrics with Constant (Scalar) Flag Curvature from Old
- 5 Geodesics of a Finsler Metric Via Navigation Problem
- 6 A New Characterization of Randers Norms
- 7 Compact Randers Metrics with Constant S-curvature
- 8 Classification Results for Randers Metrics
- 9 Construction of Randers Metrics with Isotropic S-curvature
- References
- Lorentzian Isoparametric Hypersurfaces in the Lorentzian Sphere Sn+11 Zhen-Qi Li
- 1 Introduction
- 2 Canonical Forms for Symmetric Transformation A in
- Lorentzian Space
- 3 Lorentzian Isoparametric Hypersurface of Type I in Sn+1 1
- 4 Nonexistence of Lorentzian Isoparametric Hypersurface of Type IV in Sn+1 1
- 5 Lorentzian Isoparametric Hypersurface of Type II in Sn+11
- 6 Totally Umbilical Lorentzian Isoparametric Hypersurface of Type II in Sn+1
- 7 Semi-umbilical Lorentzian Isoparametric Hypersurface of Type II in Sn+1
- 8 Non-umbilical Lorentzian Isoparametric Hypersurface of Type II in Sn+1
- References
- Asymptotically Hyperbolic Manifolds and Conformal Geometry Jie Qing
- 1 Definitions
- 2 Regularity and Rigidity for AH Manifold
- 3 Correspondences
- 4 Generalized Yamabe Problems
- References
- A Characterization of Randers Metrics of Scalar Flag Curvature Zhongmin Shen, Gulcin Civi
- 1 Introduction
- 2 Preliminaries
- 3 A Formula for the Weyl Curvature
- 4 Proof of Theorem 1.1
- 5 Weak Einstein Metrics
- 6 Proof of Theorem 1.2
- References
- Prescribed Weingarten Curvature Equations Weimin Sheng, Neil S Trudinger, Xu-Jia Wang
- 1 Introduction
- 2 The Uniform Estimate
- 3 The Gradient Estimates
- 4 The Second Order Derivative Estimate
- 5 The Dirichlet Problem
- 6 Closed Convex Hypersurfaces
- References
- Geometry Problems Related with Quasi-local Mass in General Relativity Yuguang Shi
- 1 Introduction
- 2 Quasi-local Mass on Domains with Convex Boundaries
- 3 Quasi-local Mass on Domains with Non Convex Boundary
- References
- Concerning the L4 Norms of Typical Eigenfunctions on Compact Surfaces Christopher D Sogge, Steve Zelditch
- 1 Introduction
- 2 L4 Norms of Generic Eigenfunctions
- 3 Average L4 Norms of Spherical Harmonics
- 4 L4 Norms of Orthonormal Bases of Spherical Harmonics
- 5 Random Orthonormal Bases of Spherical Harmonics
- 6 Other Orthonormal Bases
- References
- Analysis on Riemannian Manifolds with Non-convex Boundary Feng-Yu Wang
- 1 Introduction
- 2 Semigroup Properties for Curvature and Second
- Fundamental Form
- 3 Dimension-free Harnack Inequalities
- 4 Functional Inequalities
- References
- The Unity of p-harmonic Geometry Shihshu Walter Wei
- 1 Introduction
- 2 A Perspective of p-harmonic Maps
- 3 p-Harmonic Maps and Cohomology Groups
- 4 Unified Notions of F-harmonic Maps
- 5 Unified Notions of F-Yang-Mills Fields
- 6 Vector Bundle Valued p-forms on Riemannian Manifolds:A Higher Level of Generalization
- 7 Manifolds with the Global Doubling Property in p-harmonic Geometry
- 8 Generalized 1-harmonic Equations and Geometric Flows
- 9 The Mean Curvature Flow
- 10 Generalized Constant Mean Curvature Type Equations for Differential Forms
- 11 Geometric Inequalities on Manifolds
- 12 Harmonic Maps in Finsler Geometry
- References
- Hermitian Harmonic Maps Between Almost Hermitian Manifolds Xi Zhang
- 1 Introduction
- 2 Preliminary Results
- 3 Proof of Theorem 1.1
- References
- A Global Mean Value Inequality for Plurisubharmonic Functions on a Compact K¨ahler Manifold Xiaohua Zhu
- 1 Introduction
- 2 Relative Capacity and L1-estimate
- 3 Proof of Theorem 1.1
- 4 A Discussion on Theorem 1.1
- References
- A List of Publications by Professor Zhengguo Bai
- A List of Publications by Professor Yibing Shen
- A List of Graduate Students of Professors Bai and Shen
- 版权
