Sökning: "Complex Monge-Ampère equations"
Hittade 4 avhandlingar innehållade orden Complex Monge-Ampère equations.
1. Real and complex Monge-Ampère equations, statistical mechanics and canonical metrics
Sammanfattning : 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. LÄS MER
2. Regularity and boundary behavior of solutions to complex Monge–Ampère equations
Sammanfattning : In the theory of holomorphic functions of one complex variable it is often useful to study subharmonic functions. The subharmonic can be described using the Laplace operator. When one studies holomorphic functions of several complex variables one should study the plurisubharmonic functions instead. LÄS MER
3. Multipoint Okounkov bodies, strong topology of ω-plurisubharmonic functions and Kähler-Einstein metrics with prescribed singularities
Sammanfattning : The most classical topic in Kähler Geometry is the study of Kähler-Einstein metrics as solution of complex Monge-Ampère equations. This thesis principally regards the investigation of a strong topology for ω-plurisubharmonic functions on a fixed compact Kähler manifold (X,ω), its connection with complex Monge-Ampère equations with prescribed singularities and the consequent study of singular Kähler-Einstein metrics. LÄS MER
4. Topics in geometry, analysis and inverse problems
Sammanfattning : The thesis consists of three independent parts.Part I: Polynomial amoebasWe study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. LÄS MER