Evolution of Area-Decreasing Maps Between Two-Dimensional Euclidean Spaces
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Evolution of Area-Decreasing Maps Between Two-Dimensional Euclidean Spaces. / Lubbe, Felix.
I: Journal of Geometric Analysis, Bind 28, Nr. 4, 15.12.2018, s. 3928-3949.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Evolution of Area-Decreasing Maps Between Two-Dimensional Euclidean Spaces
AU - Lubbe, Felix
PY - 2018/12/15
Y1 - 2018/12/15
N2 - We consider the mean curvature flow of the graph of a smooth map f: R2→ R2 between two-dimensional Euclidean spaces. If f satisfies an area-decreasing property, the solution exists for all times and the evolving submanifold stays the graph of an area-decreasing map ft. Further, we prove uniform decay estimates for the mean curvature vector of the graph and all higher-order derivatives of the corresponding map ft.
AB - We consider the mean curvature flow of the graph of a smooth map f: R2→ R2 between two-dimensional Euclidean spaces. If f satisfies an area-decreasing property, the solution exists for all times and the evolving submanifold stays the graph of an area-decreasing map ft. Further, we prove uniform decay estimates for the mean curvature vector of the graph and all higher-order derivatives of the corresponding map ft.
KW - Area-decreasing maps
KW - Euclidean space
KW - Mean curvature flow
UR - http://www.scopus.com/inward/record.url?scp=85045133042&partnerID=8YFLogxK
U2 - 10.1007/s12220-018-0006-6
DO - 10.1007/s12220-018-0006-6
M3 - Journal article
AN - SCOPUS:85045133042
VL - 28
SP - 3928
EP - 3949
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
SN - 1050-6926
IS - 4
ER -
ID: 233725579