Hessian equations on closed Hermitian manifolds

Dekai Zhang

doi:10.2140/pjm.2017.291.485

Hessian equations on closed Hermitian manifolds

Dekai Zhang^*

^*此作品的通讯作者

University of Science and Technology of China

科研成果: 期刊稿件 › 文章 › 同行评审

37 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	485-510
页数	26
期刊	Pacific Journal of Mathematics
卷	291
期	2
DOI	https://doi.org/10.2140/pjm.2017.291.485
出版状态	已出版 - 2017
已对外发布	是

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title = "Hessian equations on closed Hermitian manifolds",

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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T1 - Hessian equations on closed Hermitian manifolds

AU - Zhang, Dekai

PY - 2017

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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

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