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arXiv · 1205.6882

Geometric properties of boundary sections of solutions to the Monge--Ampère equation and applications

Nam Q. Le·Truyen Nguyen
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Abstract

In this paper, we establish several geometric properties of boundary sections of convex solutions to the Monge-Ampère equations: the engulfing and separating properties and volume estimates. As applications, we prove a covering lemma of Besicovitch type, a covering theorem and a strong type $p-p$ estimate for the maximal function corresponding to boundary sections. Moreover, we show that the Monge-Ampère setting forms a space of homogeneous type.

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Nam Q. Le, Truyen Nguyen. 2012-05-31. Geometric properties of boundary sections of solutions to the Monge--Ampère equation and applications. https://doi.org/10.1016/j.jfa.2012.10.015

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