Regularity of geodesics in the spaces of convex and plurisubharmonic functions
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- by Soufian Abja and Sławomir Dinew PDF
- Trans. Amer. Math. Soc. 374 (2021), 3783-3800 Request permission
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 Kähler manifold setting. Finally we show a necessary and sufficient conditions for existence of a smooth geodesic between two smooth strictly convex functions.References
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Additional Information
- Soufian Abja
- Affiliation: Institute of Mathematics, Jagiellonian University, ul Lojasiewicza 6, 30-348 Kraków, Poland
- MR Author ID: 1303039
- Email: Soufian.Abja@im.uj.edu.pl
- Sławomir Dinew
- Affiliation: Institute of Mathematics, Jagiellonian University, ul Lojasiewicza 6, 30-348 Kraków, Poland
- MR Author ID: 807434
- Email: Slawomir.Dinew@im.uj.edu.pl
- Received by editor(s): June 24, 2019
- Published electronically: March 24, 2021
- Additional Notes: Both authors were supported by Polish National Science Centre grant 2017/26/E/ST1/00955
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 3783-3800
- MSC (2020): Primary 35J96; Secondary 35J70
- DOI: https://doi.org/10.1090/tran/8350
- MathSciNet review: 4251212