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Stokes' theorem in Heisenberg groups
Multi angle
Authors : Vittone, Davide (Author of the conference)
CIRM (Publisher )
26B20 - Integral formulas (Stokes, Gauss, Green, etc.)
53C17 - Sub-riemannian geometry
53C65 - Integral geometry
58C35 - "Integration on manifolds; measures on manifolds, See Also { 28Cxx}"
CIRM (Publisher )
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Abstract :
We introduce the notion of submanifolds with boundary with intrinsic $C^{1}$ regularity in the setting of sub-Riemannian Heisenberg groups. We present a Stokes' Theorem for such submanifolds involving the integration of Heisenberg differential foms introduced by Rumin. This is a joint work with M. Di Marco, A. Julia and S. Nicolussi Golo.
Keywords : Heisenberg group; manifolds with boundary; Stokes theorem; Rumins form
MSC Codes : Keywords : Heisenberg group; manifolds with boundary; Stokes theorem; Rumins form
26B20 - Integral formulas (Stokes, Gauss, Green, etc.)
53C17 - Sub-riemannian geometry
53C65 - Integral geometry
58C35 - "Integration on manifolds; measures on manifolds, See Also { 28Cxx}"
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 06/12/2024 Conference Date : 25/11/2024 Subseries : Research talks arXiv category : Differential Geometry ; Classical Analysis and ODEs ; Metric Geometry Mathematical Area(s) : Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 00:57:58 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-11-25_Vittone.mp4 
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Information on the Event
Event Title : Frontiers in Sub-Riemannian Geometry / Aux frontières de la géométrie sous-riemannienneEvent Organizers : Borza, Samuel ; Chittaro, Francesca ; Rifford, Ludovic ; Sacchelli, Ludovic ; Stefani, Giorgio Dates : 25/11/2024 - 29/11/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3091.html
Citation Data
DOI : 10.24350/CIRM.V.20272703Cite this video as: Vittone, Davide (2024). Stokes' theorem in Heisenberg groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20272703 URI : http://dx.doi.org/10.24350/CIRM.V.20272703 |
See Also
- [Multi angle] From gas giant planets to the spectral theory of subelliptic Laplacians / Author of the conference Trélat, Emmanuel.
- [Multi angle] Score matching for simulating sub-Riemannian diffusion bridge processes / Author of the conference Habermann, Karen.
- [Multi angle] Mean convex mean curvature flow in the Heisenberg group (is this related with the isoperimetric problem?) / Author of the conference Franceschi, Valentina.
- [Multi angle] Sub-Riemannian geometry of osculating curves / Author of the conference Agrachev, Andrei.
Bibliography
- DI MARCO, Marco, JULIA, Antoine, GOLO, Sebastiano Nicolussi, et al. Submanifolds with boundary and Stokes' Theorem in Heisenberg groups. arXiv preprint arXiv:2403.18675, 2024. - https://doi.org/10.48550/arXiv.2403.18675
- FRANCHI, Bruno, SERAPIONI, Raul, et CASSANO, Francesco Serra. Regular submanifolds, graphs and area formula in Heisenberg groups. Advances in mathematics, 2007, vol. 211, no 1, p. 152-203. - https://doi.org/10.1016/j.aim.2006.07.015
- FRANCHI, Bruno, TCHOU, Nicoletta, et TESI, Maria Carla. Div–curl type theorem, H-convergence and Stokes formula in the Heisenberg group. Communications in Contemporary Mathematics, 2006, vol. 8, no 01, p. 67-99. - http://doi.org/10.1142/S0219199706002039
- FRANCHI, Bruno, SERAPIONI, Raul, et CASSANO, Francesco Serra. Regular submanifolds, graphs and area formula in Heisenberg groups. Advances in mathematics, 2007, vol. 211, no 1, p. 152-203. - https://doi.org/10.1016/j.aim.2006.07.015
- RUMIN, Michel. Formes différentielles sur les variétés de contact. Journal of Differential Geometry, 1994, vol. 39, no 2, p. 281-330. - http:// doi.org/10.4310/jdg/1214454873
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