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Recently Frank & Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here ...
We show that the the image of the regular projection of a vertex of a cone over a triangle that minimizes the ratio of the cube of the area of the boundary of the cone and the square of the volume o...
Let M be an n-dimensional Riemannian manifold. We deal, mainly, with the problem of finding a relatively compact domain D ⊂⊂ M that minimizes Area(∂D) among domains of the same volum...
On surfaces we give conditions under which the solution of a restricted local isoperimetric problem for sectors with small solid angle is the circular sector and we characterize these surfaces. Also w...

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