An alexsandrov type theorem for k-convex functions

Nirmalendu Chaudhuri; Neil S. Trudinger

doi:10.1017/s0004972700038260

An alexsandrov type theorem for k-convex functions

Nirmalendu Chaudhuri^*
, Neil S. Trudinger

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this note we show that k-convex functions on ℝⁿ are twice differentiable almost everywhere for every positive integer k > n/2. This generalises Alexsandrov's classical theorem for convex functions. Copyright Clearance Centre, Inc.

Original language	English
Pages (from-to)	305-314
Number of pages	10
Journal	Bulletin of the Australian Mathematical Society
Volume	71
Issue number	2
DOIs	https://doi.org/10.1017/s0004972700038260
Publication status	Published - Apr 2005

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abstract = "In this note we show that k-convex functions on ℝn are twice differentiable almost everywhere for every positive integer k > n/2. This generalises Alexsandrov's classical theorem for convex functions. Copyright Clearance Centre, Inc.",

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AB - In this note we show that k-convex functions on ℝn are twice differentiable almost everywhere for every positive integer k > n/2. This generalises Alexsandrov's classical theorem for convex functions. Copyright Clearance Centre, Inc.

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An alexsandrov type theorem for k-convex functions

Abstract

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