《幾何與分析中的最新進展》是2012年出版的圖書，作者是東瑜昕。
基本介紹
- 中文名：幾何與分析中的最新進展
- 作者：東瑜昕
- 出版時間：2012年6月
- 頁數：522 頁
- 定價：128 元
- ISBN：9787040348255
內容簡介,目錄,
內容簡介
《幾何與分析中的最新進展》匯集了微分幾何、幾何分析、微分方程等方面一些綜述性文章或最新進展研究成果，特別有益於幾何、分析專業的碩士生、博士生以及剛剛開始從事這些領域研究的數學工作者，對在相關領域工作的其他數學工作者也很有參考價值。
目錄
Minimal Volume and Simplicial Volume of Visibility n—manifolds and All 3—manifblds
1 Introduction
2 Simplicial Volume and Bounded Cohomology
3 Visibility Manifolds and Gromov—hyperbolic Spaces
4 Gromov’S Simplicial Volume of Visibility n—manifoIds and
Compact 3—manifolds
Reference
Rigidity Theorems for Lagrangian Submanifolds of Complex Space Forms with Conformal Maslov Form
1 Introduction
2 Preliminaries
3 Rigidity Theorems for Lagrangian Submanifolds
References
Method of Moving Planes in Integral Forms and Regularity Lifting
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
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
RefeFences
Specific Non—K（a）hler Hermitian Metrics on Compact Complex
Manifolds
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
RefeFences
On the σ2—scalar Curvature and Its Applications
1 Introduction
2 σ2—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
1 Introduction
2 Local Isometric Embedding of Surfaces
3 Global Isometric Embedding of Surfaces
References
The Lagrangian Mean Curvature Flow Along the K（a）hler—Ricci Flow
1 Introduction
2 Lagrangian Property Is Preserved
RefeFences
On Magnetohydrodynamics with Partial Magnetic Dissipation near Equilibrium
1 Introduction
2 Reformulation of the Ideal MHD
3 Global Existence
4 Acknowledgement
Refefences
Hyperbolic Gradient Flow：Evolution of Graphs in Rn+1
1 Introduction
2 Hyperbolic G radient 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
1 Introduction
2 The Moser—nudinger 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
1 1 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
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+1，1
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+1，1
6 Totally Umbilical Lorentzian Isoparametric Hypersurface of Type Ⅱ in Sn+1，1
7 Semi—umbilical Lorentzian Isoparametric Hypersurface of Type Ⅱ in Sn+1，1
8 Non—umbilical Lorentzian Isoparametric Hypersurface of Type Ⅱ in Sn+1，1
References
Asymptotically Hyperbolic Manifolds and Conformal Geometry
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
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
Geometry Problems Related with Quasi—local Mass in General Relativity
Concerning the L4 Norms of Typical Eigenfunctions on Compact Surfaces
Analysis on Riemannian Manifolds with Non—convex Boundary
The Unity of p—harmonic Geometry
Hermitian Harmonic Maps Between Almost Hermitian Manifolds
A Global Mean Value Inequality for Plurisubharmonic Functions
on a Compact K（a）hler Manifold
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
RefeFences
Specific Non—K（a）hler Hermitian Metrics on Compact Complex
Manifolds
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
RefeFences
On the σ2—scalar Curvature and Its Applications
1 Introduction
2 σ2—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
1 Introduction
2 Local Isometric Embedding of Surfaces
3 Global Isometric Embedding of Surfaces
References
The Lagrangian Mean Curvature Flow Along the K（a）hler—Ricci Flow
1 Introduction
2 Lagrangian Property Is Preserved
RefeFences
On Magnetohydrodynamics with Partial Magnetic Dissipation near Equilibrium
1 Introduction
2 Reformulation of the Ideal MHD
3 Global Existence
4 Acknowledgement
Refefences
Hyperbolic Gradient Flow：Evolution of Graphs in Rn+1
1 Introduction
2 Hyperbolic G radient 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
1 Introduction
2 The Moser—nudinger 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
1 1 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
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+1，1
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+1，1
6 Totally Umbilical Lorentzian Isoparametric Hypersurface of Type Ⅱ in Sn+1，1
7 Semi—umbilical Lorentzian Isoparametric Hypersurface of Type Ⅱ in Sn+1，1
8 Non—umbilical Lorentzian Isoparametric Hypersurface of Type Ⅱ in Sn+1，1
References
Asymptotically Hyperbolic Manifolds and Conformal Geometry
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
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
Geometry Problems Related with Quasi—local Mass in General Relativity
Concerning the L4 Norms of Typical Eigenfunctions on Compact Surfaces
Analysis on Riemannian Manifolds with Non—convex Boundary
The Unity of p—harmonic Geometry
Hermitian Harmonic Maps Between Almost Hermitian Manifolds
A Global Mean Value Inequality for Plurisubharmonic Functions
on a Compact K（a）hler Manifold
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
