44 citations · 84 across the 29 of their papers we have counts for
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math.AP2008★ 1 cited
On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
Antoine Lemenant
We show that if is a global minimizer for the Mumford-Shah functional in , and if K is a smooth enough cone, then (modulo constants) u is a homogenous function of degr…
math.AP2008★ 4 cited
Regularity of the singular set for Mumford-Shah minimizers in R^3 near a minimal cone
Antoine Lemenant
We show that if (u;K) is a minimizer of the Mumford-Shah functional in an open set of R^3, and if x, K and r > 0 are such that K is close enough to a minimal cone of type P (a plan…
math.AP2008
Energy improvement for energy minimizing functions in the complement of generalized Reifenberg-flat sets
Antoine Lemenant
Let P be an hyperplane in R^N, and denote by dH the Hausdorff distance. We show that for all positive radius r < 1 there is an epsilon > 0, such that if K is a Reifenberg-flat set…