Object

Title: Forced Flow by Powers of the $\emph{m}^{\th}$ Mean Curvature

Publication Details:

Established in 2008

Journal or Publication Title:

Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես

Date of publication:

2010

Volume:

3

Number:

2

ISSN:

1829-1163

Official URL:


Contributor(s):

Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան

Coverage:

61-91

Abstract:

In this paper, we consider the $m^{\th}$ mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. Under the assumption that the initial hypersurface is suitably pinched, we show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all time and expand to infinity if the forcing term is large enough. The flow can also converge to a round sphere for some special forcing term and initial hypersurface. Furthermore, the normalization of the flow is carried out so that long time existence and convergence of the rescaled flow are studied. Our work extends Schulze's flow by powers of the mean curvature and Cabezas-Rivas and Sinestrari's volume-preserving flow by powers of the $m^{\th}$ mean curvature.

Publisher:

National Academy of Sciences of Armenia

Date created:

2010-06-17

Format:

pdf

Identifier:

oai:arar.sci.am:13240

General note:

Electronic Open Access Publication of the National Academy of Sciences of Armenia

Digitization:

ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան

Location of original object:

ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան

Object collections:

Last modified:

Apr 19, 2024

In our library since:

Feb 12, 2020

Number of object content hits:

21

All available object's versions:

https://arar.sci.am/publication/14944

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