Ce papier caractérise sur les variétés riemanniennes compactes les fonctions a variation bornée á l’aide d’asymptotiques en temps petit du semigroupe de la chaleur. En particulier, on montre comment la variation totale d’une fonction peut être calculée à partir du noyau de la chaleur. Nous utilisons deux approches disjointes, une approche probabiliste et une approche analytique ; ces deux approches ont des avantages différents et potentiellement peuvent être généralisées dans des contextes distincts.
This paper provides a characterization of functions of bounded variation (BV) in a compact Riemannian manifold in terms of the short time behavior of the heat semigroup. In particular, the main result proves that the total variation of a function equals the limit characterizing the space BV. The proof is carried out following two fully independent approaches, a probabilistic and an analytic one; each method presents different advantages.
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@article{AFST_2023_6_32_3_577_0,
author = {Patricia Alonso Ruiz and Fabrice Baudoin},
title = {Yet another heat semigroup characterization of {BV} functions on {Riemannian} manifolds},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {577--606},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 32},
number = {3},
year = {2023},
doi = {10.5802/afst.1745},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1745/}
}
TY - JOUR AU - Patricia Alonso Ruiz AU - Fabrice Baudoin TI - Yet another heat semigroup characterization of BV functions on Riemannian manifolds JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2023 SP - 577 EP - 606 VL - 32 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1745/ DO - 10.5802/afst.1745 LA - en ID - AFST_2023_6_32_3_577_0 ER -
%0 Journal Article %A Patricia Alonso Ruiz %A Fabrice Baudoin %T Yet another heat semigroup characterization of BV functions on Riemannian manifolds %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2023 %P 577-606 %V 32 %N 3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1745/ %R 10.5802/afst.1745 %G en %F AFST_2023_6_32_3_577_0
Patricia Alonso Ruiz; Fabrice Baudoin. Yet another heat semigroup characterization of BV functions on Riemannian manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 3, pp. 577-606. doi : 10.5802/afst.1745. https://afst.centre-mersenne.org/articles/10.5802/afst.1745/
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