scholarly journals On a mixed Monge–Ampère operator for quasiplurisubharmonic functions with analytic singularities

2019 ◽  
Vol 52 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Richard Lärkäng ◽  
Martin Sera ◽  
Elizabeth Wulcan
Keyword(s):  
Analytic Singularities ◽  
Monge Ampere

scholarly journals On a Monge-Ampere operator for plurisubharmonic functions with analytic singularities

2019 ◽  
Vol 68 (4) ◽  
pp. 1217-1231 ◽  
Author(s):  
Matts Andersson ◽  
Zbigniew Blocki ◽  
Elizabeth Wulcan
Keyword(s):  
Plurisubharmonic Functions ◽  
Analytic Singularities ◽  
Monge Ampere

scholarly journals Pluricomplex Green's functions and Fano manifolds

2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Nicholas McCleerey ◽  
Valentino Tosatti
Keyword(s):  
Green's Functions ◽  
Einstein Metrics ◽  
Green’S Functions ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Continuity Method ◽  
Homogeneous Complex ◽  
Analytic Singularities ◽  
Kähler Einstein Metrics ◽  
Monge Ampere

We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Ampere equation on its complement, confirming an expectation of Tian-Yau. Comment: EpiGA Volume 3 (2019), Article Nr. 9

scholarly journals The exterior Dirichlet problems of Monge–Ampère equations in dimension two

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Limei Dai
Keyword(s):  
Asymptotic Behavior ◽  
Unit Ball ◽  
Bounded Domain ◽  
Viscosity Solutions ◽  
Sufficient Conditions ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Necessary And Sufficient ◽  
Monge Ampere ◽  
Prescribed Asymptotic Behavior

AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ det D 2 u = f in dimension two with f being a perturbation of $f_{0}$ f 0 at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.

Monge–Ampère of Pac-Man

2019 ◽  
Vol 114 (3) ◽  
pp. 343-352
Author(s):  
Norm Levenberg ◽  
Sione Ma’u
Keyword(s):  
Monge Ampere

scholarly journals Monge–Ampère measures on subvarieties

2015 ◽  
Vol 423 (1) ◽  
pp. 94-105 ◽  
Author(s):  
Per Åhag ◽  
Urban Cegrell ◽  
Hoàng Hiệp Phạm
Keyword(s):  
Monge Ampere

scholarly journals An inequality for mixed Monge–Ampère measures

2008 ◽  
Vol 262 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Sławomir Dinew
Keyword(s):  
Monge Ampere
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