دانلود کتاب Geometric Analysis of Quasilinear Inequalities on Complete Manifolds (Frontiers in Mathematics)

فهرست مطالب :

Preface
Contents
List of Symbols
1 Some Geometric Motivations
1.1 Prescribing the Mean Curvature of a Graph
The Seeming Lack of a Keller–Osserman Condition
Geodesic Graphs in R h M
Mean Curvature Flow Solitons
Equidistant Graphs in M h R
1.2 A Problem from the Theory of Stochastic Control
2 An Overview of Our Results
2.1 Setting and Main Properties Under Investigation
2.2 Keller–Osserman Conditions
2.3 Notation and Conventions
2.4 The Finite Maximum Principle (FMP)
2.5 Strong and Weak Maximum Principles at Infinity
2.6 The Strong Liouville Property (SL)
2.7 The Compact Support Principle (CSP)
2.8 More General Inequalities
3 Preliminaries from Riemannian Geometry
3.1 Model Manifolds
3.2 Comparison Theory for the Distance Function
4 Radialization and Fake Distances
4.1 Basic Facts on Nonlinear Potential Theory
Model Manifolds
Uniqueness and Comparison Theory for G
4.2 The Fake Distance and Its Basic Properties
Relations with Hardy Weights
4.3 Gradient Estimate
4.4 Properness of
5 Boundary Value Problems for Nonlinear ODEs
5.1 The Dirichlet Problem
5.2 The Mixed Dirichlet–Neumann Problem
6 Comparison Results and the Finite Maximum Principle
6.1 Basic Comparisons and a Pasting Lemma
6.2 The Finite Maximum Principle
7 Weak Maximum Principle and Liouville\'s Property
7.1 The Equivalence Between (WMP∞) and (L)
7.2 Volume Growth and (WMP∞)
7.3 Bernstein Theorems for Minimal and MCF Soliton Graphs
7.4 Counterexamples
8 Strong Maximum Principle and Khas\'minskii Potentials
8.1 Ricci Curvature and (SMP∞)
8.2 Bernstein Theorems for Prescribed Mean Curvature Graphs
9 The Compact Support Principle
9.1 Necessity of (KO0) for the Compact Support Principle
9.2 Sufficiency of (KO0) for the Compact Support Principle
General Operators and No Cut-Locus
A Second ODE Lemma: Locating the Support
Non-Empty Cut-Locus: The p-Laplacian Case
A Further Fake Distance and the Feller Property
Proof of Proposition 9.19
10 Keller–Osserman, A Priori Estimates and the (SL) Property
10.1 Necessity of (KO∞) for the (SL) Property
10.2 Sufficiency of (KO∞) for the (SL) Property
10.3 Ricci Curvature and (SL)
10.4 Sharpness
10.5 Volume Growth and (SL)
10.6 Applications: Yamabe and Capillarity Equations
Yamabe Type Equations
The Capillarity Equation
10.7 Other Ranges of Parameters
Bibliography
Index