路易斯·尼伦伯格著季理真主编的《微分方程和微分几何(英文版)(精)》是著名的数学家在其研究鼎盛时期所写的有关偏微分方程和微分几何的著作。分成两部分。第I部分讨论了椭圆微分方程解的存在性和唯一性，简洁、切中要点，叙述流畅，体现了著名数学家对所写材料的深刻理解。第II部分所讨论的议题对于很多读者，甚至微分几何方面的专家都是新的。本书篇幅短小精悍，却包含丰富的内容。可供对本领域感兴趣的读者参考。

Part I Existence Theorems in Partial Differential Equations
1 Preliminaries
1.1 Introduction
1.2 The Maximum Principle
1.3 Consequences of the Maximum Principle
2 The Potential Equation
2.1 Fundamental Solution
2.2 The Poisson Integral Formula
2.3 The Mean Value Property of Potential Functions
2.4 Estimates of Derivatives of Harmonic Functions and
Analyticity
2.5 The Theorems and Inequality of Harnack
2.6 Theorem on Removable Singularities
3 The Perron Method for Solving the Dirichlet Problem
3.1 The Perron Method
3.2 The Perron Method for More General Elliptic Equations
4 Schauder Estimates
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 Boundary Value 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 Form of 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 Theorem 2.1
3 On Surfaces with Constant Negative Gauss Curvature
3.1 Hilbert's Theorem on Hyperbolic 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 Theorem of Christoffel on Closed Surfaces
10 Minkowski's Problem
11 Existence of a Closed Convex Surface Solving Minkowski's
Problem