The purpose of these lecture notes is to provide an introduction to the theory of complex Monge-Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary).These operators are of centra…
The purpose of these lecture notes is to provide an introduction to the theory of complex Monge-Ampere operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of centr…
Annotation The purpose of these lecture notes is to provide an introduction to the theory of complex MongeAmpère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators ar…
1. Classical differential geometry -- 2. Foundation of geometry -- 3. Geometric algebra -- 4. Riemannian geometry -- 5. Closed geodesies "This set of selected papers of Klingenberg covers some of the important mathematical aspects of Riemannian Geometry, Closed Geodesics, Geome…
This set of selected papers of Klingenberg covers some of the important mathematical aspects of Riemannian Geometry, Closed Geodesics, Geometric Algebra, Classical Differential Geometry and Foundations of Geometry of Klingenberg. Of significance were his contributions to Riemann…
This monograph presents an approachable proof of Mirzakhani's curve counting theorem, both for simple and non-simple curves. Designed to welcome readers to the area, the presentation builds intuition with elementary examples before progressing to rigorous proofs.
"This monograph presents an approachable proof of Mirzakhani’s curve counting theorem, both for simple and non-simple curves. Designed to welcome readers to the area, the presentation builds intuition with elementary examples before progressing to rigorous proofs. This approach …
This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patte…
"This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patt…
This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both…