We prove that if is a minimizer of the Mumford-Shah functional in an open set of , and if and are such that is close enough to a minimal cone of type (a plane), (three half planes meeting at with 120 angles) or (cone over the 6 edges of a regular tetrahedron centered at ) in terms of Hausdorff distance in , then is equivalent to the minimal cone in where is a universal constant.
@article{ASNSP_2011_5_10_3_561_0, author = {Lemenant, Antoine}, title = {Regularity of the singular set for {Mumford-Shah} minimizers in $\protect \mathbb{R}^3$ near a minimal cone}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {561--609}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 10}, number = {3}, year = {2011}, mrnumber = {2905379}, zbl = {1239.49062}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2011_5_10_3_561_0/} }
TY - JOUR AU - Lemenant, Antoine TI - Regularity of the singular set for Mumford-Shah minimizers in $\protect \mathbb{R}^3$ near a minimal cone JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2011 SP - 561 EP - 609 VL - 10 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2011_5_10_3_561_0/ LA - en ID - ASNSP_2011_5_10_3_561_0 ER -
%0 Journal Article %A Lemenant, Antoine %T Regularity of the singular set for Mumford-Shah minimizers in $\protect \mathbb{R}^3$ near a minimal cone %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2011 %P 561-609 %V 10 %N 3 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2011_5_10_3_561_0/ %G en %F ASNSP_2011_5_10_3_561_0
Lemenant, Antoine. Regularity of the singular set for Mumford-Shah minimizers in $\protect \mathbb{R}^3$ near a minimal cone. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 3, pp. 561-609. http://www.numdam.org/item/ASNSP_2011_5_10_3_561_0/
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