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An Alexsandrov type theorem for k-convex functions

Published online by Cambridge University Press:  17 April 2009

Nirmalendu Chaudhuri  and
Neil S. Trudinger
Nirmalendu Chaudhuri
Affiliation:
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200Australia e-mail: chaudhur@maths.anu.edu.au, neil.trudinger@maths.anu.edu.au
Neil S. Trudinger
Affiliation:
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200Australia e-mail: chaudhur@maths.anu.edu.au, neil.trudinger@maths.anu.edu.au
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 305 - 314
Copyright
Copyright © Australian Mathematical Society 2005

References

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