most citedExistence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

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math.DG2003★ 6 cited

Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

Manuel Ritoré, César Rosales

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence…

math.DG2003

Least-perimeter partitions of the disk into three regions of given areas

Antonio Cañete, Manuel Ritoré

We prove that the unique least-perimeter way of partitioning the unit 2-dimensional disk into three regions of prescribed areas is by means of the standard graph consisting in thre…

math.DG2003

From constant mean curvature hypersurfaces to the gradient theory of phase transitions

Frank Pacard, Manuel Ritoré

We construct solutions of the Cahn-Hilliard equation whose nodal set converges to a given constant mean curvature hypersurface in a Riemannian manifold.