SL(n) Invariant Valuations on Super-Coercive Convex Functions. (25th February 2021) - Mussnig, Fabian
Abstract: All non-negative, continuous, SL(n), and translation invariant valuations on the space of super-coercive, convex functions on R^n are classified. Furthermore, using the invariance of the function space under the Legendre transform, a classification of non-negative, continuous, 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.