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math.OC2016
Isoperimetry with upper mean curvature bounds and sharp stability estimates
Brian Krummel, Francesco Maggi
It was proved by Almgren that among boundaries whose mean curvature is bounded from above, perimeter is uniquely minimized by balls. We obtain sharp stability estimates for Almgren…
math.OC2016
Existence and almost everywhere regularity of isoperimetric clusters for fractional perimeters
Maria Colombo, Francesco Maggi
The existence of minimizers in the fractional isoperimetric problem with multiple volume constraints is proved, together with a partial regularity result.
math.OC2015
Stability for the Brunn-Minkowski and Riesz rearrangement inequalities, with applications to Gaussian concentration and finite range non-local isoperimetry
Eric A. Carlen, Francesco Maggi
We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. W…