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arXiv · 1906.01386

Regularity of geodesics in the spaces of convex and plurisubharmonic functions

Soufian Abja·Slawomir Dinew
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Abstract

In this note we investigate the regularity of geodesics in the space of convex and plurisubharmonic functions. In the real setting we prove (optimal) local C^{1,1} regularity. We construct examples which prove that the global C^{1,1} regularity fails both in the real and complex case in contrast to the K\"ahler manifold setting. Finally we show a necessary and sufficient conditions for existence of a smooth geodesic between two smooth strictly convex functions.

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Soufian Abja, Slawomir Dinew. 2019-06-04. Regularity of geodesics in the spaces of convex and plurisubharmonic functions. https://arxiv.org/abs/1906.01386

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