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Geometric Viewpoint of L∞ Estimates for Linearized Monge-Ampère Equations
Abstract
We prove a Harnack inequality on Monge--Ampère gradient graphs under suitable geometric bounds, giving us interior L∞ 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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BibTeX
@misc{rakshit2026geometric,
title = {{Geometric Viewpoint of $L^\infty$ Estimates for Linearized Monge-Ampère Equations}},
author = {Arghya Rakshit and Derek Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23848},
eprint = {2610.23848},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23848},
}
RIS
TY - UNPB
TI - Geometric Viewpoint of L^∞ Estimates for Linearized Monge-Ampère Equations
AU - Arghya Rakshit
AU - Derek Wu
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23848
UR - https://arxiv.org/abs/2610.23848
AB - We prove a Harnack inequality on Monge--Ampère gradient graphs under suitable geometric bounds, giving us interior L^∞ 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.
ER -