Geometric Analysis combines differential equations and differential geometry. An important aspect is to solve geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Ampere equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications. This handbook of geometric analysis provides introductions to and surveys of important topics in geometric analysis and their applications to related fields which is intend to be referred by graduate students and researchers in related areas.
- Front Matter
- Birational geometry for nilpotent orbits Yoshinori Namikawa
- Cell decompositions of moduli space, lattice points and Hurwitz problems Paul Norbury
- Moduli of abelian varieties in mixed and in positive characteristic Frans Oort
- Local models of Shimura varieties, IGeometry and combinatorics Georgios Pappas, Michael Rapoport and Brian Smithling
- Generalized theta linear series on moduli spaces of vector bundles on curves Mihnea Popa
- Computer aided unirationality proofs of moduli spaces Frank-Olaf Schreyer
- Deformation theory from the point of view of fibered categories Mattia Talpo and Angelo Vistoli
- Mumford’s conjecture — a topological outlook Ulrike Tillmann
- Rational parametrizations of moduli spaces of curves Alessandro Verra
- Hodge loci Claire Voisin
- Homological stability for mapping class groups of surfaces Nathalie Wahl
- 版权
