Sökning: "Complex Monge-Ampère operator"

Visar resultat 6 - 9 av 9 avhandlingar innehållade orden Complex Monge-Ampère operator.

1. 6. Boundary values of plurisubharmonic functions and related topics

   Författare :Berit Kemppe; Urban Cegrell; Anders Fällström; Alexander Raskovskii; Umeå universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Plurisubharmonic functions; boundary measures; boundary values; complex Monge-Ampère operator; weak*-convergence; Mathematical analysis; Analys; Mathematics; matematik;

   Sammanfattning : This thesis consists of three papers concerning problems related to plurisubharmonic functions on bounded hyperconvex domains, in particular boundary values of such functions. The papers summarized in this thesis are:* Paper I Urban Cegrell and Berit Kemppe, Monge-Ampère boundary measures, Ann. Polon. Math. LÄS MER

3. 7. The plurisubharmonic Mergelyan property

   Författare :Lisa Hed; Urban Cegrell; Anders Fällström; Per Åhag; Jan Wiegerinck; Umeå universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Complex Monge-Ampère operator; approximation; plurisubharmonic function; subextension; Mergelyan property; plurisubharmonic function on compact sets; Jensen measures; Mathematics; matematik;

   Sammanfattning : In this thesis, we study two different kinds of approximation of plurisubharmonic functions. The first one is a Mergelyan type approximation for plurisubharmonic functions. LÄS MER

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

   Författare :Antonio Trusiani; Chalmers tekniska högskola; []
   Nyckelord :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;

   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

5. 9. Boundary singularities of plurisubharmonic functions

   Författare :Mårten Nilsson; Matematik LTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; pluripotential theory; envelope of plurisubharmonic functions; complex Monge-Ampère equation; Jensen measures;

   Sammanfattning : We study the Perron–Bremermann envelope P(μ, φ):=sup{u(z) ; u ∈ PSH(Ω), (ddcu)n≥ μ, u^* ≤ φ} on a B-regular domain Ω. Such envelopes occupy a central position within pluripotential theory as they, for suitable μ and φ harmonic and continuous on the closure of Ω, constitute unique solutions to the Dirichlet problem for the complex Monge–Ampère operator. LÄS MER