Details
| Original language | English |
|---|---|
| Pages (from-to) | 213-230 |
| Number of pages | 18 |
| Journal | Mathematische Annalen |
| Volume | 333 |
| Issue number | 1 |
| Publication status | Published - 14 Jun 2005 |
Abstract
This paper is concerned with the following three types of geometric evolution equations: the volume preserving mean curvature flow, the intermediate surface diffusion flow, and the surface diffusion flow. Important common properties of these flows are the preservation of volume and the decrease of perimeter. It is shown in this paper that the intermediate surface diffusion flow can lose convexity. Hence the volume preserving mean curvature flow is the only flow among the evolution equations under consideration which preserves convexity, cf. [11, 16, 14, 17]. Moreover, several sufficient conditions are presented, which illustrate that each of the above mentioned flows can move smooth initial configurations into singularities in finite time.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Annalen, Vol. 333, No. 1, 14.06.2005, p. 213-230.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Some dynamic properties of volume preserving curvature driven flows
AU - Escher, Joachim
AU - Ito, Kazuo
PY - 2005/6/14
Y1 - 2005/6/14
N2 - This paper is concerned with the following three types of geometric evolution equations: the volume preserving mean curvature flow, the intermediate surface diffusion flow, and the surface diffusion flow. Important common properties of these flows are the preservation of volume and the decrease of perimeter. It is shown in this paper that the intermediate surface diffusion flow can lose convexity. Hence the volume preserving mean curvature flow is the only flow among the evolution equations under consideration which preserves convexity, cf. [11, 16, 14, 17]. Moreover, several sufficient conditions are presented, which illustrate that each of the above mentioned flows can move smooth initial configurations into singularities in finite time.
AB - This paper is concerned with the following three types of geometric evolution equations: the volume preserving mean curvature flow, the intermediate surface diffusion flow, and the surface diffusion flow. Important common properties of these flows are the preservation of volume and the decrease of perimeter. It is shown in this paper that the intermediate surface diffusion flow can lose convexity. Hence the volume preserving mean curvature flow is the only flow among the evolution equations under consideration which preserves convexity, cf. [11, 16, 14, 17]. Moreover, several sufficient conditions are presented, which illustrate that each of the above mentioned flows can move smooth initial configurations into singularities in finite time.
UR - http://www.scopus.com/inward/record.url?scp=23044514255&partnerID=8YFLogxK
U2 - 10.1007/s00208-005-0671-1
DO - 10.1007/s00208-005-0671-1
M3 - Article
AN - SCOPUS:23044514255
VL - 333
SP - 213
EP - 230
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 1
ER -