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