| Issue |
ESAIM: COCV
Volume 32, 2026
|
|
|---|---|---|
| Article Number | 61 | |
| Number of page(s) | 19 | |
| DOI | https://doi.org/10.1051/cocv/2026043 | |
| Published online | 14 July 2026 | |
The Brøndsted–Rockafellar theorem in geodesic spaces
1
Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz,
Heinrichstraße 36,
8010
Graz,
Austria
2
Institut für Stochastik und Wirtschaftsmathematik, Technische Universität Wien,
Wiedner Hauptstraße 8, VADOR E105-04,
1040
Wien,
Austria
3
Departamento de Matemáticas, Universidad de Sonora,
Hermosillo,
Sonora
83000,
Mexico
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
11
November
2025
Accepted:
29
May
2026
Abstract
We present a constructive version of the Brøndsted–Rockafellar theorem in general geodesic metric spaces. Applications include a constructive form of the Caristi theorem and quantitative relations between metric slope error bounds and the global growth of functionals.
Mathematics Subject Classification: 47H10 / 49J52 / 49K27 / 49Q22 / 51F99
Key words: Variational principle,Wasserstein space / geodesic metric space / Brøndsted–Rockafellar / Carlier inequality
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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