Work

Geometric Viewpoint of $L^\infty$ Estimates for Linearized Monge-Ampère Equations

Year: 2026

Type: preprint

Abstract: We prove a Harnack inequality on Monge--Ampère gradient graphs under suitable geometric bounds, giving us interior $L^\infty$ estimates for the linearized Monge--Ampère equation. The proof combines Moser iteration on extrensic balls with a gradient estimate for the extrinsic distance function. The argument avoids the Caffarelli--Gutiérrez Harnack inequality and the engulfing and covering properties of Monge--Ampère sections.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.23848

Authors: Rakshit, Arghya, Wu, Derek

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7222961608

Cites: 3

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Related to: 10