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arXiv · 1903.04225

$\operatorname{SL}(n)$ invariant valuations on super-coercive convex functions

Fabian Mussnig
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Abstract

All non-negative, continuous, $\operatorname{SL}(n)$ and translation invariant valuations on the space of super-coercive, convex functions on $\mathbb{R}^n$ are classified. Furthermore, using the invariance of the function space under the Legendre transform, a classification of non-negative, continuous, $\operatorname{SL}(n)$ and dually translation invariant valuations is obtained. In both cases, different functional analogs of the Euler characteristic, volume and polar volume are characterized.

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Fabian Mussnig. 2019-03-11. $\operatorname{SL}(n)$ invariant valuations on super-coercive convex functions. https://doi.org/10.4153/s0008414x19000531

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