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Generalized minimizing movements for the varifold Canham–Helfrich flow

  • Katharina Brazda , Martin Kružík ORCID logo und Ulisse Stefanelli ORCID logo EMAIL logo
Veröffentlicht/Copyright: 13. Januar 2024

Abstract

The gradient flow of the Canham–Helfrich functional is tackled via the generalized minimizing movements approach. We prove the existence of solutions in Wasserstein spaces of varifolds, as well as upper and lower diameter bounds. In the more regular setting of multiply covered C 1 , 1 surfaces, we provide a Li–Yau-type estimate for the Canham–Helfrich energy and prove the conservation of multiplicity along the evolution.


Communicated by Frank Duzaar


Funding statement: This work has been partially supported by the Austrian Science Fund (FWF) project F 65 and by the BMBWF through the OeAD WTZ projects CZ04/2019 and CZ01/2021, as well as their Czech counterpart MŠMT ČR project 8J21AT001. K. Brazda acknowledges the support by the DFG-FWF international joint project FR 4083/3-1/I 4354 and the FWF project W 1245. M. Kružík is indebted to the E. Schrödinger Institute for Mathematics and Physics for its hospitality during his stay in Vienna in 2022. He also acknowledges support by the GAČR-FWF project 21-06569. K. U. Stefanelli also acknowledges support from the FWF projects I 5149 and P 32788.

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Received: 2022-07-07
Accepted: 2023-09-20
Published Online: 2024-01-13
Published in Print: 2024-07-01

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