On EVI flows for the spherical Hellinger distance and the spherical Hellinger-Kantorovich distance
speaker: Alexander Mielke (WIAS, Berlin)abstract: The Hellinger distance (sometimes also called Fisher-Rao distance) and the Hellinger-Kantorovich distance are geodesic distances on the set of all non-negative measures. The spherical case reduces these geodesic distances to geodesic distances on the set of probability measures.
In the spherical case, the analysis of gradient systems is more difficult, because of the non-local term in the metric tensor. We discuss strategies how geodesic convexity the spherical Hellinger space and the spherical Hellinger-Kantorovich space can be inferred from the easier non-spherical case. EVI flows are constructed via the generation technique of Savaré-Muratori by suitably localizing the construction to either the sublevels of the energy or to kappa-concave subsets.
The discussed results relies on to joint works with Vaios Laschos, Matthias Liero, Giuseppe Savaré, Oliver Tse, and Jia-Jie Zhu.
timetable:
Fri 6 Dec, 12:00 - 12:45, Aula Dini
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