1 Table of Contents: “... and Thorn Classes -- 2 Asymptotic Expansion of the Heat Kernel -- 2.1 Differential Operators -- 2.2 The Heat...”

2 Table of Contents: “... and Kinematic Measure. The Heat Kernel for Compact Manifolds. The Dirichlet Heat Kernel for Regular Domains...”

3 Table of Contents: “... and related topics -- Isoperimetric methods -- Isoperimetric methods and the heat equation -- Geometric...”

4 Table of Contents: “...1. Geometric preliminaries -- 2. Some principles of analysis -- 3. The heat flow on manifolds...”

5 Table of Contents: “... -- 4. First-order calculus on metric measure spaces -- 5. Heat flow on metric measure spaces -- 6...”

6 Table of Contents: “...Cauchy uniqueness in the Riemannian obstacle problem -- Non-abelian hodge theory via heat flow...”

7 Table of Contents: “...Analysis on Fractals -- Heat Kernels on Metric Spaces with Doubling Measure -- Self-similarity...”

8 Table of Contents: “... of Maps and Metrics -- Heat Flow into Spheres for a Class of Energies -- Singularity Models for the Ricci...”

9 Table of Contents: “.... The nonlinear Laplacian -- 12. The Bochner-Weitzenbock formula -- 13. Nonlinear heat flow -- 14. Gradient...”

10 Table of Contents: “... and the hypoelliptic Laplacian -- Xianzhe Dai and Richard Melrose, Adiabatic limits, heat kernels and analytic torsion...”

11 Table of Contents: “...Chapter 1. On the Bumpy Fundamental Group Scheme -- Chapter 2. Heat Kernels, Bergman Kernels...”

12 Table of Contents: “... of Kaehlerian manifolds -- Isoperimetric inequalities, heat equation and geometric applications -- Symmetric...”

13 Table of Contents: “... for maximization of heat transfer under weight constraints -- The "Graph Theory" of the Greek Alphabet...”

14 Table of Contents: “...1. The heat equation approach to Hermitian-Einstein metrics on stable bundles -- §1. Definition...”

15 Table of Contents: “... to Determinant Bundles Using (Heat-kernel) Renormalization Techniques -- I. Renormalization techniques -- II...”

16 “... inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel...”

17 “...­ voted to Hodge theory for the transversal Laplacian and applications of the heat equation method...”

18 “... operator and the heat flow method; as well as the most important variational principles of theoretical...”

19 “... based on the heat equation. Later chapters deal with recent developments on isospectrality, Sunada’s...”