Regularization of m-subharmonic functions and Hölder continuity

Jingrui Cheng; Yulun Xu

doi:10.4310/MRL.241118233017

Regularization of m-subharmonic functions and Hölder continuity

Jingrui Cheng
, Yulun Xu

Mathematics

Stony Brook University

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

1 Scopus citations

Abstract

We use sup-convolution to find upper approximations of a bounded m-subharmonic function on a compact Kähler manifold with nonnegative holomorphic bisectional curvature. As an application, we show the Hölder continuity of solutions to σ_m equation when the right hand side is in L^p, (Formula presented). All these results generalize to more general complex Hessian equations.

Original language	English
Pages (from-to)	951-984
Number of pages	34
Journal	Mathematical Research Letters
Volume	31
Issue number	4
DOIs	https://doi.org/10.4310/MRL.241118233017
State	Published - 2024

Access to Document

10.4310/MRL.241118233017

Cite this

@article{aa178fb02e1048b2b2667067008d89f4,

title = "Regularization of m-subharmonic functions and H{\"o}lder continuity",

abstract = "We use sup-convolution to find upper approximations of a bounded m-subharmonic function on a compact K{\"a}hler manifold with nonnegative holomorphic bisectional curvature. As an application, we show the H{\"o}lder continuity of solutions to σm equation when the right hand side is in Lp, (Formula presented). All these results generalize to more general complex Hessian equations.",

author = "Jingrui Cheng and Yulun Xu",

year = "2024",

doi = "10.4310/MRL.241118233017",

language = "English",

volume = "31",

pages = "951--984",

journal = "Mathematical Research Letters",

issn = "1073-2780",

number = "4",

}

TY - JOUR

T1 - Regularization of m-subharmonic functions and Hölder continuity

AU - Cheng, Jingrui

AU - Xu, Yulun

PY - 2024

Y1 - 2024

N2 - We use sup-convolution to find upper approximations of a bounded m-subharmonic function on a compact Kähler manifold with nonnegative holomorphic bisectional curvature. As an application, we show the Hölder continuity of solutions to σm equation when the right hand side is in Lp, (Formula presented). All these results generalize to more general complex Hessian equations.

AB - We use sup-convolution to find upper approximations of a bounded m-subharmonic function on a compact Kähler manifold with nonnegative holomorphic bisectional curvature. As an application, we show the Hölder continuity of solutions to σm equation when the right hand side is in Lp, (Formula presented). All these results generalize to more general complex Hessian equations.

UR - https://www.scopus.com/pages/publications/85216291661

U2 - 10.4310/MRL.241118233017

DO - 10.4310/MRL.241118233017

M3 - Article

AN - SCOPUS:85216291661

SN - 1073-2780

VL - 31

SP - 951

EP - 984

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 4

ER -

Regularization of m-subharmonic functions and Hölder continuity

Abstract

Access to Document

Other files and links

Fingerprint

Cite this