Heterotopic energy for Sobolev mappings
(2026) Communications in Contemporary Mathematics — Vol. 28, n° 05, p. 2640006 (2026)
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- Authors
Detaille, Antoine 
- Abstract
- We study the notion of heterotopic energy defined as the limit of Sobolev energies of Sobolev mappings in a given homotopy class approximating almost everywhere a given Sobolev mapping. We show that the heterotopic energy is finite if and only if the mappings in the corresponding homotopy classes are homotopic on a codimension one skeleton of a triangulation of the domain. When this is the case, the heterotopic energy of a mapping is the sum of its Sobolev energy and its disparity energy, defined as the minimum energy of a bubble to pass between these homotopy classes. At the more technical level, we rely on a framework that works when the target and domain manifolds are not simply connected and there is no canonical isomorphism between homotopy groups with different basepoints.
- Affiliations
Citations
Detaille, A., & Van Schaftingen, J. (2026). Heterotopic energy for Sobolev mappings. Communications in Contemporary Mathematics, 28(05), 2640006. https://doi.org/10.1142/S0219199726400067 (Original work published 2026)