Some aspects of the variational nature of mean curvature flow

Bellettini, Giovanni, and Mugnai, Luca. "Some aspects of the variational nature of mean curvature flow." Journal of the European Mathematical Society 010.4 (2008): 1013-1036. <http://eudml.org/doc/277238>.

@article{Bellettini2008,
abstract = {We show that the classical solution of the heat equation can be seen as the minimizer of a suitable functional defined in space-time. Using similar ideas, we introduce a functional $\mathcal \{F\}$ on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related with $\mathcal \{F\}$. We show some connections between minimizers of $\mathcal \{F\}$ and mean curvature flow.},
author = {Bellettini, Giovanni, Mugnai, Luca},
journal = {Journal of the European Mathematical Society},
keywords = {heat equation; space-time energy minimizers; mean curvature flow; heat equation; space-time energy minimizers; mean curvature flow},
language = {eng},
number = {4},
pages = {1013-1036},
publisher = {European Mathematical Society Publishing House},
title = {Some aspects of the variational nature of mean curvature flow},
url = {http://eudml.org/doc/277238},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Bellettini, Giovanni
AU - Mugnai, Luca
TI - Some aspects of the variational nature of mean curvature flow
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 4
SP - 1013
EP - 1036
AB - We show that the classical solution of the heat equation can be seen as the minimizer of a suitable functional defined in space-time. Using similar ideas, we introduce a functional $\mathcal {F}$ on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related with $\mathcal {F}$. We show some connections between minimizers of $\mathcal {F}$ and mean curvature flow.
LA - eng
KW - heat equation; space-time energy minimizers; mean curvature flow; heat equation; space-time energy minimizers; mean curvature flow
UR - http://eudml.org/doc/277238
ER -