TY - JOUR
T1 - Avoidance for set-theoretic solutions of mean-curvature-type flows
AU - Hershkovits, Or
AU - White, Brian
N1 - Publisher Copyright:
© 2023 International Press of Boston, Inc.. All rights reserved.
PY - 2023/9/21
Y1 - 2023/9/21
N2 - We give a self-contained treatment of set-theoretic subsolutions to flow by mean curvature, or, more generally, to flow by mean curvature plus an ambient vector field. The ambient space can be any smooth Riemannian manifold. Most importantly, we show that if two such set-theoretic subsolutions are initially disjoint, then they remain disjoint provided one of the subsolutions is compact; previously, this was only known for Euclidean space (with no ambient vectorfield). We also give a simple proof of a version of Ilmanen’s interpolation theorem.
AB - We give a self-contained treatment of set-theoretic subsolutions to flow by mean curvature, or, more generally, to flow by mean curvature plus an ambient vector field. The ambient space can be any smooth Riemannian manifold. Most importantly, we show that if two such set-theoretic subsolutions are initially disjoint, then they remain disjoint provided one of the subsolutions is compact; previously, this was only known for Euclidean space (with no ambient vectorfield). We also give a simple proof of a version of Ilmanen’s interpolation theorem.
UR - http://www.scopus.com/inward/record.url?scp=85174895118&partnerID=8YFLogxK
U2 - 10.4310/CAG.2023.V31.N1.A2
DO - 10.4310/CAG.2023.V31.N1.A2
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85174895118
SN - 1019-8385
VL - 31
SP - 31
EP - 67
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
IS - 1
ER -