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A sharp quantitative Alexandrov inequality and applications to volume preserving geometric flows in 3D
Vesa Julin, Massimiliano Morini, Francesca Oronzio +1
We study the asymptotic behavior of the volume preserving mean curvature and the Mullins-Sekerka flat flow in three dimensional space. Motivated by this we establish a 3D sharp qua…
Rigidity and large volume residues in exterior isoperimetry for convex sets
Nicola Fusco, Francesco Maggi, Massimiliano Morini +1
A comparison theorem by Choe, Ghomi and Ritoré states that the exterior isoperimetric profile of any convex body in lies above that of…
The Asymptotics of the Area-Preserving Mean Curvature and the Mullins-Sekerka Flow in Two Dimensions
Vesa Julin, Massimiliano Morini, Marcello Ponsiglione +1
We provide the first general result for the asymptotics of the area preserving mean curvature flow in two dimensions showing that flat flow solutions, starting from any bounded set…
Total positive curvature and the equality case in the relative isoperimetric inequality outside convex domains
Nicola Fusco, Massimiliano Morini
We settle the case of equality for the relative isoperimetric inequality outside any arbitrary convex set with not empty interior.