Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 175-186 |
| Seitenumfang | 12 |
| Fachzeitschrift | Mathematische Nachrichten |
| Jahrgang | 229 |
| Publikationsstatus | Veröffentlicht - 1 Jan. 2001 |
| Extern publiziert | Ja |
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, Jahrgang 229, 01.01.2001, S. 175-186.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -