The Largest Eigenvalue of a Convex Function, Duality, and a Theorem of Slodkowski

First, we provide an exposition of a theorem due to Slodkowski regarding the largest “eigenvalue” of a convex function. In his work on the Dirichlet problem, Slodkowski introduces a generalized second-order derivative which for C 2 functions corresponds to the largest eigenvalue of the Hessian. The...

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Bibliographic Details
Published in:	The Journal of geometric analysis Vol. 26; no. 4; pp. 3027 - 3055
Main Author:	Dellatorre, Matthew
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.10.2016 Springer Nature B.V
Subjects:	Abstract Harmonic Analysis Convex and Discrete Geometry Convexity Differential Geometry Dirichlet problem Dynamical Systems and Ergodic Theory Eigenvalues Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Lower bounds Mathematics Mathematics and Statistics Theorems 52A41 35J60 Dualilty 26B25 Convex analysis Legendre transform estimates
ISSN:	1050-6926, 1559-002X
Online Access:	Get full text
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