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arXiv · 2610.23848

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

Arghya Rakshit·Derek Wu
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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.

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Arghya Rakshit, Derek Wu. 2026-10-16. Geometric Viewpoint of $L^\infty$ Estimates for Linearized Monge-Ampère Equations. https://arxiv.org/abs/2610.23848

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