《几何与分析中的最新进展(精)》编著者东瑜昕等。

　　《几何与分析中的最新进展》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。

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