Details
| Original language | English |
|---|---|
| Pages (from-to) | 253-260 |
| Number of pages | 8 |
| Journal | Analysis (Germany) |
| Volume | 30 |
| Issue number | 3 |
| Publication status | Published - 26 Jul 2010 |
Abstract
The gradient flow of the surface functional of compact hypersurfaces with respect to the inner product of L2 is described by the evolution of surfaces by their mean curvature. This type of flows have been studied using methods from differential geometry and the theory of partial differential equations as well. In this paper we are interested in the evolution of surfaces obtained by rotating the graph of a positive and periodic function around the abscissa. The main result of this work completes the studies presented in [2] and [5]. More precisely, we prove that for periodic surfaces with non-negative mean curvature satisfying a natural monotonicity property the solution to the mean curvature flow blows up in finite time in the sense that neck pinching occurs.
Keywords
- Mean curvature flow, neck pinching, parabolic maximum principle
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Applied Mathematics
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In: Analysis (Germany), Vol. 30, No. 3, 26.07.2010, p. 253-260.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Neck pinching for periodic mean curvature flows
AU - Escher, Joachim
AU - Matioc, Bogdan-Vasile
PY - 2010/7/26
Y1 - 2010/7/26
N2 - The gradient flow of the surface functional of compact hypersurfaces with respect to the inner product of L2 is described by the evolution of surfaces by their mean curvature. This type of flows have been studied using methods from differential geometry and the theory of partial differential equations as well. In this paper we are interested in the evolution of surfaces obtained by rotating the graph of a positive and periodic function around the abscissa. The main result of this work completes the studies presented in [2] and [5]. More precisely, we prove that for periodic surfaces with non-negative mean curvature satisfying a natural monotonicity property the solution to the mean curvature flow blows up in finite time in the sense that neck pinching occurs.
AB - The gradient flow of the surface functional of compact hypersurfaces with respect to the inner product of L2 is described by the evolution of surfaces by their mean curvature. This type of flows have been studied using methods from differential geometry and the theory of partial differential equations as well. In this paper we are interested in the evolution of surfaces obtained by rotating the graph of a positive and periodic function around the abscissa. The main result of this work completes the studies presented in [2] and [5]. More precisely, we prove that for periodic surfaces with non-negative mean curvature satisfying a natural monotonicity property the solution to the mean curvature flow blows up in finite time in the sense that neck pinching occurs.
KW - Mean curvature flow
KW - neck pinching
KW - parabolic maximum principle
UR - http://www.scopus.com/inward/record.url?scp=85016677014&partnerID=8YFLogxK
U2 - 10.1524/anly.2010.1039
DO - 10.1524/anly.2010.1039
M3 - Article
AN - SCOPUS:85016677014
VL - 30
SP - 253
EP - 260
JO - Analysis (Germany)
JF - Analysis (Germany)
SN - 0174-4747
IS - 3
ER -