Hessian estimates for the sigma-2 equation in dimension four

Ravi Shankar; Yu Yuan

doi:10.4007/annals.2025.201.2.4

Hessian estimates for the sigma-2 equation in dimension four

Ravi Shankar, Yu Yuan

Mathematics

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

3 Scopus citations

Abstract

We derive a priori interior Hessian estimates and interior regularity for the σ2 equation in dimension four. Our method provides both a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher (n ≥ 5) dimensions.

Original language	English (US)
Pages (from-to)	489-513
Number of pages	25
Journal	Annals of Mathematics
Volume	201
Issue number	2
DOIs	https://doi.org/10.4007/annals.2025.201.2.4
State	Published - 2025

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

Keywords

interior estimates
k-Hessian equation
regularity

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10.4007/annals.2025.201.2.4

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title = "Hessian estimates for the sigma-2 equation in dimension four",

abstract = "We derive a priori interior Hessian estimates and interior regularity for the σ2 equation in dimension four. Our method provides both a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher (n ≥ 5) dimensions.",

keywords = "interior estimates, k-Hessian equation, regularity",

author = "Ravi Shankar and Yu Yuan",

note = "Publisher Copyright: {\textcopyright} 2025 Department of Mathematics, Princeton University.",

year = "2025",

doi = "10.4007/annals.2025.201.2.4",

language = "English (US)",

volume = "201",

pages = "489--513",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Department of Mathematics at Princeton University",

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TY - JOUR

T1 - Hessian estimates for the sigma-2 equation in dimension four

AU - Shankar, Ravi

AU - Yuan, Yu

PY - 2025

Y1 - 2025

N2 - We derive a priori interior Hessian estimates and interior regularity for the σ2 equation in dimension four. Our method provides both a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher (n ≥ 5) dimensions.

AB - We derive a priori interior Hessian estimates and interior regularity for the σ2 equation in dimension four. Our method provides both a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher (n ≥ 5) dimensions.

KW - interior estimates

KW - k-Hessian equation

KW - regularity

UR - https://www.scopus.com/pages/publications/105000428646

UR - https://www.scopus.com/inward/citedby.url?scp=105000428646&partnerID=8YFLogxK

U2 - 10.4007/annals.2025.201.2.4

DO - 10.4007/annals.2025.201.2.4

M3 - Article

AN - SCOPUS:105000428646

SN - 0003-486X

VL - 201

SP - 489

EP - 513

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 2

ER -

Hessian estimates for the sigma-2 equation in dimension four

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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