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A note on Alxesandrov type theorem for k-convex functions

Nirmalendu Chaudhuri·Neil S. Trudinger
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Abstract

In this note we show that $k$-convex functions on $\Bbb R^n$ are twice differentiable almost everywhere for every positive integer $k>n/2$. This generalizes the classical Alexsandrov's theorem for convex functions.

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Nirmalendu Chaudhuri, Neil S. Trudinger. 2004-11-01. A note on Alxesandrov type theorem for k-convex functions. https://arxiv.org/abs/math/0411036

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