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
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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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A flow approach to the prescribed Gaussian curvature problem in ℍ𝑛+1
- A split special Lagrangian calibration associated with frame vorticity
- The homogeneous causal action principle on a compact domain in momentum space
- The Lp Minkowski problem for q-torsional rigidity
- A twist in sharp Sobolev inequalities with lower order remainder terms
- Least energy solutions for affine p-Laplace equations involving subcritical and critical nonlinearities
- Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains
- Existence of minimizers for the SDRI model in 2d: Wetting and dewetting regime with mismatch strain
- Generalized minimizing movements for the varifold Canham–Helfrich flow
- A characterization of gauge balls in ℍ n by horizontal curvature
- Minimizers of 3D anisotropic interaction energies
- Regularity results for a class of widely degenerate parabolic equations
- On isosupremic vectorial minimisation problems in L ∞ with general nonlinear constraints
- Quasiconformal, Lipschitz, and BV mappings in metric spaces
- Continuous differentiability of a weak solution to very singular elliptic equations involving anisotropic diffusivity
- Optimal transport with nonlinear mobilities: A deterministic particle approximation result
- On functions of bounded β-dimensional mean oscillation
- Relaxed many-body optimal transport and related asymptotics
- Minimizers of nonlocal polyconvex energies in nonlocal hyperelasticity
Articles in the same Issue
- Frontmatter
- A flow approach to the prescribed Gaussian curvature problem in ℍ𝑛+1
- A split special Lagrangian calibration associated with frame vorticity
- The homogeneous causal action principle on a compact domain in momentum space
- The Lp Minkowski problem for q-torsional rigidity
- A twist in sharp Sobolev inequalities with lower order remainder terms
- Least energy solutions for affine p-Laplace equations involving subcritical and critical nonlinearities
- Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains
- Existence of minimizers for the SDRI model in 2d: Wetting and dewetting regime with mismatch strain
- Generalized minimizing movements for the varifold Canham–Helfrich flow
- A characterization of gauge balls in ℍ n by horizontal curvature
- Minimizers of 3D anisotropic interaction energies
- Regularity results for a class of widely degenerate parabolic equations
- On isosupremic vectorial minimisation problems in L ∞ with general nonlinear constraints
- Quasiconformal, Lipschitz, and BV mappings in metric spaces
- Continuous differentiability of a weak solution to very singular elliptic equations involving anisotropic diffusivity
- Optimal transport with nonlinear mobilities: A deterministic particle approximation result
- On functions of bounded β-dimensional mean oscillation
- Relaxed many-body optimal transport and related asymptotics
- Minimizers of nonlocal polyconvex energies in nonlocal hyperelasticity