6533b836fe1ef96bd12a0a62

RESEARCH PRODUCT

Volume preserving mean curvature flows near strictly stable sets in flat torus

Joonas Niinikoski

subject

osittaisdifferentiaaliyhtälötMean curvature53C44 (Primary) and 35K93 (Secondary)Applied Mathematics010102 general mathematicsMathematical analysisSense (electronics)Stability result01 natural sciences010101 applied mathematicsSet (abstract data type)differentiaaligeometriastrictly stable setsMathematics - Analysis of PDEsFlow (mathematics)Volume (thermodynamics)Independent setFOS: Mathematics0101 mathematicsFlat torusAnalysisMathematicsperiodic stabilityvolume preserving mean curvature flowAnalysis of PDEs (math.AP)

description

In this paper we establish a new stability result for the smooth volume preserving mean curvature flow in flat torus $\mathbb T^n$ in low dimensions $n=3,4$. The result says roughly that if the initial set is near to a strictly stable set in $\mathbb T^n$ in $H^3$-sense, then the corresponding flow has infinite lifetime and converges exponentially fast to a translate of the strictly stable (critical) set in $W^{2,5}$-sense.

yearjournalcountryeditionlanguage
2021-03-01
https://dx.doi.org/10.48550/arxiv.1907.03618