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

Found 4 swedish dissertations containing the words Complex Monge-Ampère equations.

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

    Author : Jakob Hultgren; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; 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. Regularity and boundary behavior of solutions to complex Monge–Ampère equations

    Author : Björn Ivarsson; Zbigniew Blocki; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Complex Monge--Ampère operator; interior regularity; plurisubharmonic function; blow-up rate of solutions; bounded plurisubharmonic exhaustion function; globally Lipschitz; strongly pseudoconvex domain; hyperconvex domain; Bergman kernel; MATEMATIK; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Abstract : 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. READ MORE

  5. 3. Multipoint Okounkov bodies, strong topology of ω-plurisubharmonic functions and Kähler-Einstein metrics with prescribed singularities

    Author : Antonio Trusiani; Chalmers tekniska högskola; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Okounkov bodies; Seshadri constant; Kähler-Einstein metrics; Kähler Geometry; Canonical metrics; Fano manifolds; Pluripotential theory; Complex Monge-Ampère equations; Kähler packing;

    Abstract : 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. READ MORE

  6. 4. Topics in geometry, analysis and inverse problems

    Author : Hans Rullgård; Mikael Passare; Victor Palamodov; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Laurent series; Harnack curves; differential equations; tomography; Mathematical logic; Matematisk logik;

    Abstract : 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. READ MORE