Search for dissertations about: "Real Monge-Ampère equations"

Found 2 swedish dissertations containing the words Real Monge-Ampère equations.

2. 1. Real and complex Monge-Ampère equations, statistical mechanics and canonical metrics

   Author : Jakob Hultgren; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Statistical Mechanics; Point Processes; Hessian manifolds; Kähler geometry; Optimal Transport; Canonical metrics; Complex Monge-Ampère equations; Real Monge-Ampère equations; Kähler-Einstein metrics; Statistical Mechanics;

   Abstract : Recent decades has seen a strong trend in complex geometry to study canonical metrics and the way they relate to geometric analysis, algebraic geometry and probability theory. This thesis consists of four papers each contributing to this field. The first paper sets up a probabilistic framework for real Monge-Ampère equations on tori. READ MORE

4. 2. Permanental Point Processes on Real Tori

   Author : Jakob Hultgren; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Point Processes; Monge-Ampère equations; Affine Manifolds; Point Processes;

   Abstract : The main motivation for this thesis is to study real Monge-Ampère equations. These are fully nonlinear differential equations that arise in differential geometry. They lie at the heart of optimal transport and, as such, are related to probability theory, statistics, geometrical inequalities, fluid dynamics and diffusion equations. READ MORE