Details
| Original language | English |
|---|---|
| Pages (from-to) | 175-186 |
| Number of pages | 12 |
| Journal | Mathematische Nachrichten |
| Volume | 229 |
| Publication status | Published - 1 Jan 2001 |
| Externally published | Yes |
Abstract
We derive a one to one correspondence between conformal solitons of the mean curvature flow in an ambient space N and minimal submanifolds in a different ambient space Ñ, where Ñ equals ℝ x N equipped with a warped product metric and show that a submanifold in N converges to a conformai soliton under the mean curvature flow in N if and only if its associated submanifold in Ñ converges to a minimal submanifold under a rescaled mean curvature flow in Ñ. We then define a notion of stability for conformai solitons and obtain Lp estimates as well as pointwise estimates for the curvature of stable solitons.
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In: Mathematische Nachrichten, Vol. 229, 01.01.2001, p. 175-186.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A relation between mean curvature flow solitons and minimal submanifolds
AU - Smoczyk, Knut
PY - 2001/1/1
Y1 - 2001/1/1
N2 - We derive a one to one correspondence between conformal solitons of the mean curvature flow in an ambient space N and minimal submanifolds in a different ambient space Ñ, where Ñ equals ℝ x N equipped with a warped product metric and show that a submanifold in N converges to a conformai soliton under the mean curvature flow in N if and only if its associated submanifold in Ñ converges to a minimal submanifold under a rescaled mean curvature flow in Ñ. We then define a notion of stability for conformai solitons and obtain Lp estimates as well as pointwise estimates for the curvature of stable solitons.
AB - We derive a one to one correspondence between conformal solitons of the mean curvature flow in an ambient space N and minimal submanifolds in a different ambient space Ñ, where Ñ equals ℝ x N equipped with a warped product metric and show that a submanifold in N converges to a conformai soliton under the mean curvature flow in N if and only if its associated submanifold in Ñ converges to a minimal submanifold under a rescaled mean curvature flow in Ñ. We then define a notion of stability for conformai solitons and obtain Lp estimates as well as pointwise estimates for the curvature of stable solitons.
KW - Mean curvature flow
KW - Solitons
UR - http://www.scopus.com/inward/record.url?scp=0035661405&partnerID=8YFLogxK
U2 - 10.1002/1522-2616(200109)229:1<175::AID-MANA175>3.0.CO;2-H
DO - 10.1002/1522-2616(200109)229:1<175::AID-MANA175>3.0.CO;2-H
M3 - Article
AN - SCOPUS:0035661405
VL - 229
SP - 175
EP - 186
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
ER -