Hessian equations on closed Hermitian manifolds

Dekai Zhang

doi:10.2140/pjm.2017.291.485

Hessian equations on closed Hermitian manifolds

Dekai Zhang

University of Science and Technology of China

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

We solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the Kähler case proven by Hou, Ma and Wu and Dinew and Kolodziej. Solving the equation can be reduced to the derivation of a priori second-order estimates. We introduce a new method to prove the C⁰ estimate. The C² estimate can be derived if we use the auxiliary function which is mainly due to Hou, Ma and Wu and Tosatti and Weinkove.

Original language	English
Pages (from-to)	485-510
Number of pages	26
Journal	Pacific Journal of Mathematics
Volume	291
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2017.291.485
State	Published - 2017
Externally published	Yes

Keywords

A priori estimates
Closed Hermitian manifolds
Hessian equations

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10.2140/pjm.2017.291.485

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abstract = "We solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the K{\"a}hler case proven by Hou, Ma and Wu and Dinew and Kolodziej. Solving the equation can be reduced to the derivation of a priori second-order estimates. We introduce a new method to prove the C0 estimate. The C2 estimate can be derived if we use the auxiliary function which is mainly due to Hou, Ma and Wu and Tosatti and Weinkove.",

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year = "2017",

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AU - Zhang, Dekai

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N2 - We solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the Kähler case proven by Hou, Ma and Wu and Dinew and Kolodziej. Solving the equation can be reduced to the derivation of a priori second-order estimates. We introduce a new method to prove the C0 estimate. The C2 estimate can be derived if we use the auxiliary function which is mainly due to Hou, Ma and Wu and Tosatti and Weinkove.

AB - We solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the Kähler case proven by Hou, Ma and Wu and Dinew and Kolodziej. Solving the equation can be reduced to the derivation of a priori second-order estimates. We introduce a new method to prove the C0 estimate. The C2 estimate can be derived if we use the auxiliary function which is mainly due to Hou, Ma and Wu and Tosatti and Weinkove.

KW - A priori estimates

KW - Closed Hermitian manifolds

KW - Hessian equations

UR - https://www.scopus.com/pages/publications/85030029667

U2 - 10.2140/pjm.2017.291.485

DO - 10.2140/pjm.2017.291.485

M3 - 文章

AN - SCOPUS:85030029667

SN - 0030-8730

VL - 291

SP - 485

EP - 510

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

Hessian equations on closed Hermitian manifolds

Abstract

Keywords

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