Stationary sets of the mean curvature flow with a forcing term
Julin, V., & Niinikoski, J. (2023). Stationary sets of the mean curvature flow with a forcing term. Advances in Calculus of Variations, 16(2), 391-402. https://doi.org/10.1515/acv-2021-0019
Published in
Advances in Calculus of VariationsDate
2023Discipline
MatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)Copyright
© 2021 Walter de Gruyter GmbH
We consider the flat flow solution to the mean curvature equation with forcing in ℝn. Our main resultstates that tangential balls in ℝn under a flat flow with a bounded forcing term will experience fattening, which generalizes the result in [N. Fusco, V. Julin and M. Morini, Stationary sets and asymptotic behavior ofthe mean curvature flow with forcing in the plane, preprint (2020), https://arxiv.org/abs/2004.07734] from the planar case to higher dimensions. Then, as in the planar case, we characterize stationary sets in ℝn for a constant forcing term as finite unions of equisize balls with mutually positive distance.
Publisher
Walter de Gruyter GmbHISSN Search the Publication Forum
1864-8258Keywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/99233805
Metadata
Show full item recordCollections
License
Related items
Showing items with similar title or keywords.
-
Stationary Sets and Asymptotic Behavior of the Mean Curvature Flow with Forcing in the Plane
Fusco, Nicola; Julin, Vesa; Morini, Massimiliano (Springer, 2022)We consider the flat flow solutions of the mean curvature equation with a forcing term in the plane. We prove that for every constant forcing term the stationary sets are given by a finite union of disks with equal radii ... -
Asymptotical behavior of volume preserving mean curvature flow and stationary sets of forced mean curvature flow
Niinikoski, Joonas (Jyväskylän yliopisto, 2021)The main subject of this dissertation is mean curvature type of flows, in particular the volume preserving mean curvature flow. A classical flow in this context is seen as a smooth time evolution of n-dimensional sets. An ... -
Consistency of the Flat Flow Solution to the Volume Preserving Mean Curvature Flow
Julin, Vesa; Niinikoski, Joonas (Springer, 2024)We consider the flat flow solution, obtained via a discrete minimizing movement scheme, to the volume preserving mean curvature flow starting from C1,1-regular set. We prove the consistency principle, which states that ... -
Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds
Nobili, Francesco; Violo, Ivan Yuri (Elsevier, 2024)We study the qualitative stability of two classes of Sobolev inequalities on Riemannian manifolds. In the case of positive Ricci curvature, we prove that an almost extremal function for the sharp Sobolev inequality is close ... -
A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition
Liu, Jiayin; Zhang, Shijin; Zhou, Yuan (Elsevier, 2024)We build up a quantitative second-order Sobolev estimate of lnw for positive p-harmonic functions w in Riemannian manifolds under Ricci curvature bounded from below and also for positive weighted p-harmonic functions w in ...