Details
| Original language | English |
|---|---|
| Pages (from-to) | 455-473 |
| Number of pages | 19 |
| Journal | Advances in mathematics |
| Volume | 255 |
| Publication status | Published - 1 Apr 2014 |
Abstract
Let f : M → N be a smooth area decreasing map between two Riemannian manifolds (M, gM) and (N, gN). Under weak and natural assumptions on the curvatures of (M, gM) and (N, gN), we prove that the mean curvature flow provides a smooth homotopy of f to a constant map.
Keywords
- Area decreasing, Graphs, Homotopy, Maximum principle, Mean curvature flow
ASJC Scopus subject areas
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In: Advances in mathematics, Vol. 255, 01.04.2014, p. 455-473.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Homotopy of area decreasing maps by mean curvature flow
AU - Savas-Halilaj, Andreas
AU - Smoczyk, Knut
PY - 2014/4/1
Y1 - 2014/4/1
N2 - Let f : M → N be a smooth area decreasing map between two Riemannian manifolds (M, gM) and (N, gN). Under weak and natural assumptions on the curvatures of (M, gM) and (N, gN), we prove that the mean curvature flow provides a smooth homotopy of f to a constant map.
AB - Let f : M → N be a smooth area decreasing map between two Riemannian manifolds (M, gM) and (N, gN). Under weak and natural assumptions on the curvatures of (M, gM) and (N, gN), we prove that the mean curvature flow provides a smooth homotopy of f to a constant map.
KW - Area decreasing
KW - Graphs
KW - Homotopy
KW - Maximum principle
KW - Mean curvature flow
UR - http://www.scopus.com/inward/record.url?scp=84893424143&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2014.01.014
DO - 10.1016/j.aim.2014.01.014
M3 - Article
AN - SCOPUS:84893424143
VL - 255
SP - 455
EP - 473
JO - Advances in mathematics
JF - Advances in mathematics
SN - 0001-8708
ER -