Suppose that is a closed countably -rectifiable set whose complement consists of more than one connected component. Assume that the -dimensional Hausdorff measure of is finite or grows at most exponentially near infinity. Under these assumptions, we prove a global-in-time existence of mean curvature flow in the sense of Brakke starting from . There exists a finite family of open sets which move continuously with respect to the Lebesgue measure, and whose boundaries coincide with the space-time support of the mean curvature flow.
Supposons que est un ensemble dénombrable fermé -rectifiable dont le complément n’est pas connexe. Nous assumons que la mesure de Hausdorff -dimensionnelle de est finie ou sa croissance est au plus exponentielle. Nous prouvons l’existence globale du flot de la courbure moyenne au sens de Brakke au départ de . Il existe une famille finie d’ensembles ouverts qui se déplacent d’une manière continue par rapport à la mesure de Lebesgue et dont les bords coïncident avec le support du flot de la courbure moyenne.
Revised:
Accepted:
Published online:
Keywords: mean curvature flow, varifold, geometric measure theory
Mot clés : mouvement par courbure moyenne, varifold, théorie de la mesure géométrique
Kim, Lami 1; Tonegawa, Yoshihiro 1
@article{AIF_2017__67_1_43_0, author = {Kim, Lami and Tonegawa, Yoshihiro}, title = {On the mean curvature flow of grain boundaries}, journal = {Annales de l'Institut Fourier}, pages = {43--142}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {67}, number = {1}, year = {2017}, doi = {10.5802/aif.3077}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3077/} }
TY - JOUR AU - Kim, Lami AU - Tonegawa, Yoshihiro TI - On the mean curvature flow of grain boundaries JO - Annales de l'Institut Fourier PY - 2017 SP - 43 EP - 142 VL - 67 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3077/ DO - 10.5802/aif.3077 LA - en ID - AIF_2017__67_1_43_0 ER -
%0 Journal Article %A Kim, Lami %A Tonegawa, Yoshihiro %T On the mean curvature flow of grain boundaries %J Annales de l'Institut Fourier %D 2017 %P 43-142 %V 67 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3077/ %R 10.5802/aif.3077 %G en %F AIF_2017__67_1_43_0
Kim, Lami; Tonegawa, Yoshihiro. On the mean curvature flow of grain boundaries. Annales de l'Institut Fourier, Volume 67 (2017) no. 1, pp. 43-142. doi : 10.5802/aif.3077. https://aif.centre-mersenne.org/articles/10.5802/aif.3077/
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