Complex Hessian equations with prescribed singularity on compact Kahler manifolds

被引：0

作者：

Lu, Chinh H. ^{[1
]}

Nguyen, Van-don

机构：

[1] Univ Paris Saclay, CNRS, Lab Math dOrsay, F-91405 Orsay, France

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2022年 / 23卷 / 01期

关键词：

MONGE-AMPERE EQUATIONS; DIRICHLET PROBLEM; VARIATIONAL APPROACH; VISCOSITY SOLUTIONS; ELLIPTIC-EQUATIONS; METRIC GEOMETRY; MONOTONICITY; ENVELOPES; ENERGY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (X, co) be a compact Kahler manifold of dimension n and fix 1 < m < n. We prove that the total mass of the complex Hessian measure of co- m-subharmonic functions is non-decreasing with respect to the singularity type. We then solve complex Hessian equations with prescribed singularity, and prove a Hodge index type inequality for positive currents.

引用

页码：425 / 462

页数：38

共 65 条

[1] Quaternionic Monge-AmpSre equation and Calabi problem for HKT-manifolds [J].

Alesker, S. ;

Verbitsky, M. .

ISRAEL JOURNAL OF MATHEMATICS, 2010, 176 (01) :109-138

[2]

[Anonymous], 2004, Asian J. Math.

[3]

AUBIN T, 1978, B SCI MATH, V102, P63

[4] FINE TOPOLOGY, SILOV BOUNDARY, AND (DDC)N [J].

BEDFORD, E ;

TAYLOR, BA .

JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 72 (02) :225-251

[5] DIRICHLET PROBLEM FOR A COMPLEX MONGE-AMPERE EQUATION [J].

BEDFORD, E ;

TAYLOR, BA .

INVENTIONES MATHEMATICAE, 1976, 37 (01) :1-44

[6] A NEW CAPACITY FOR PLURISUBHARMONIC-FUNCTIONS [J].

BEDFORD, E ;

TAYLOR, BA .

ACTA MATHEMATICA, 1982, 149 (1-2) :1-40

[7] From Monge-Ampere equations to envelopes and geodesic rays in the zero temperature limit [J].

Berman, Robert J. .

MATHEMATISCHE ZEITSCHRIFT, 2019, 291 (1-2) :365-394

[8] A VARIATIONAL APPROACH TO COMPLEX MONGE-AMPERE EQUATIONS [J].

Berman, Robert J. ;

Boucksom, Sebastien ;

Guedj, Vincent ;

Zeriahi, Ahmed .

PUBLICATIONS MATHEMATIQUES DE L IHES, 2013, (117) :179-245

[9] Weak solutions to the complex Hessian equation [J].

Blocki, Z .

ANNALES DE L INSTITUT FOURIER, 2005, 55 (05) :1735-+

[10] Monge-Ampere equations in big cohomology classes [J].

Boucksom, Sebastien ;

Eyssidieux, Philippe ;

Guedj, Vincent ;

Zeriahi, Ahmed .

ACTA MATHEMATICA, 2010, 205 (02) :199-262

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