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Lectures on Differential Equations and Differential Geometry 微分方程和微分几何 （英文版）

样章
作者：
Louis Nirenberg （路易斯·尼伦伯格 ）
定价：
89.00元
ISBN：
978-7-04-050302-9
版面字数：
300.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2018-09-25
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：
偏微分方程
暂无
  • Front Matter
  • Part I Existence Theorems in Partial Differential Equations
    • 1 Preliminaries.
      • 1.1 Introduction.
      • 1.2 TheMaximumPrinciple
      • 1.3 Consequences of theMaximumPrinciple
    • 2 The Potential Equation
      • 2.1 Fundamental Solution
      • 2.2 The Poisson Integral Formula
      • 2.3 TheMean Value Property of Potential Functions
      • 2.4 Estimates of Derivatives of Harmonic Functions and Analyticity
      • 2.5 The Theorems and Inequality ofHarnack
      • 2.6 Theoremon Removable Singularities
    • 3 The PerronMethod for Solving the Dirichlet Problem
      • 3.1 The PerronMethod
      • 3.2 The PerronMethod forMore General Elliptic Equations
    • 4 SchauderEstimates.
      • 4.1 Poisson’s Equation
      • 4.2 A Preliminary Estimate
      • 4.3 Statement of Schauder’s Estimates
      • 4.4 Some Applications of the Interior Estimates
      • 4.5 The BoundaryValue Problem
      • 4.6 Strong Barrier Functions, and the Boundary Value Problem
    • 5 Derivation of the Schauder Estimates
      • 5.1 A Preliminary Estimate
      • 5.2 A Further Investigation of the Poisson Equation
      • 5.3 Completion of the Interior Estimates
  • Part II Seminar on Differential Geometry in the Large
    • 1 Complete Surfaces
    • 2 The Formof Complete Surfaces of Positive Gauss Curvature in Three-dimensional Space
      • 2.1 Hadamard’s Principle
      • 2.2 Completeness of a Surface
      • 2.3 Examples Showing that the Properties V , V _ and E are Independent
      • 2.4 Main Theorem.
      • 2.5 Consequence
      • 2.6 Analogous Theorems for Plane Curves
      • 2.7 Proof of Theorem2.1
    • 3 On Surfaces with Constant Negative Gauss Curvature
      • 3.1 Hilbert’s TheoremonHyperbolic Surfaces
      • 3.2 Asymptotic Coordinates in the Small
      • 3.3 Considerations in the Large.
      • 3.4 Bounds on the Extended Angle Function.
    • 4 Isometric Deformations in the Small
    • 5 Rigidity of Closed Convex Surfaces
    • 6 Rigid Open Convex Surfaces
    • 7 Rigidity of Sphere
    • 8 Uniqueness of Closed Convex Surfaces with Prescribed Line Element
    • 9 A Theoremof Christoffel on Closed Surfaces
    • 10 Minkowski’s Problem
    • 11 Existence of a Closed Convex Surface Solving Minkowski’s Problem
  • About the author

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