Geodesic convexity of small neighborhood in the space of Kähler potentials

Xiuxiong Chen; Mikhail Feldman; Jingchen Hu

doi:10.1016/j.jfa.2020.108603

Geodesic convexity of small neighborhood in the space of Kähler potentials

Xiuxiong Chen
, Mikhail Feldman
, Jingchen Hu

Mathematics

University of Wisconsin-Madison
University of Science and Technology of China
ShanghaiTech University

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

5 Scopus citations

Abstract

We show that, given k>4, [Formula presented], any point in the space of non-degenerate smooth Kähler potentials has a small neighborhood with respect to C^k norm, s.t. any two points in this neighborhood can be connected by a geodesic of at least C^k−J regularity.

Original language	English
Article number	108603
Journal	Journal of Functional Analysis
Volume	279
Issue number	7
DOIs	https://doi.org/10.1016/j.jfa.2020.108603
State	Published - Oct 15 2020

Keywords

Degenerate complex Monge-Ampère equation
Kähler geometry
Nash-Moser inverse function theorem
Riemann-Hilbert problem

Access to Document

10.1016/j.jfa.2020.108603

Cite this

@article{74866acfec144d1fbce8a1664cdc271c,

title = "Geodesic convexity of small neighborhood in the space of K{\"a}hler potentials",

abstract = "We show that, given k>4, [Formula presented], any point in the space of non-degenerate smooth K{\"a}hler potentials has a small neighborhood with respect to Ck norm, s.t. any two points in this neighborhood can be connected by a geodesic of at least Ck−J regularity.",

keywords = "Degenerate complex Monge-Amp{\`e}re equation, K{\"a}hler geometry, Nash-Moser inverse function theorem, Riemann-Hilbert problem",

author = "Xiuxiong Chen and Mikhail Feldman and Jingchen Hu",

note = "Publisher Copyright: {\textcopyright} 2020",

year = "2020",

month = oct,

day = "15",

doi = "10.1016/j.jfa.2020.108603",

language = "English",

volume = "279",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

number = "7",

}

TY - JOUR

T1 - Geodesic convexity of small neighborhood in the space of Kähler potentials

AU - Chen, Xiuxiong

AU - Feldman, Mikhail

AU - Hu, Jingchen

PY - 2020/10/15

Y1 - 2020/10/15

N2 - We show that, given k>4, [Formula presented], any point in the space of non-degenerate smooth Kähler potentials has a small neighborhood with respect to Ck norm, s.t. any two points in this neighborhood can be connected by a geodesic of at least Ck−J regularity.

AB - We show that, given k>4, [Formula presented], any point in the space of non-degenerate smooth Kähler potentials has a small neighborhood with respect to Ck norm, s.t. any two points in this neighborhood can be connected by a geodesic of at least Ck−J regularity.

KW - Degenerate complex Monge-Ampère equation

KW - Kähler geometry

KW - Nash-Moser inverse function theorem

KW - Riemann-Hilbert problem

UR - https://www.scopus.com/pages/publications/85087395683

U2 - 10.1016/j.jfa.2020.108603

DO - 10.1016/j.jfa.2020.108603

M3 - Article

AN - SCOPUS:85087395683

SN - 0022-1236

VL - 279

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 7

M1 - 108603

ER -

Geodesic convexity of small neighborhood in the space of Kähler potentials

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this