20 citations · 77 across the 14 of their papers we have counts for
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Obstacles and Singularities of Riemannian Distance Functions
Paolo Albano, Piermarco Cannarsa, Carlo Sinestrari
We study the distance function from a point target in the complement of a compact obstacle endowed with a smooth Riemannian metric. We prove that the obstacle necessarily generates…
Generation of singularities from the initial datum for Hamilton-Jacobi equations
Paolo Albano, Piermarco Cannarsa, Carlo Sinestrari
We study the generation of singularities from the initial datum for a solution of the Cauchy problem for a class of Hamilton-Jacobi equations of evolution. For such equations, we g…
Convex sets evolving by volume preserving fractional mean curvature flows
Eleonora Cinti, Carlo Sinestrari, Enrico Valdinoci
We consider the volume preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curva…
Global Propagation of Singularities for Time Dependent Hamilton-Jacobi Equations
Piermarco Cannarsa, Marco Mazzola, Carlo Sinestrari
We investigate the properties of the set of singularities of semiconcave solutions of Hamilton-Jacobi equations of the form \begin{equation*} u_t(t,x)+H(\nabla u(t,x))=0, \qquad\te…
Singular gradient flow of the distance function and homotopy equivalence
Paolo Albano, Piermarco Cannarsa, Khai Tien Nguyen +1
It is a generally shared opinion that significant information about the topology of a bounded domain of a riemannian manifold is encoded into the properties of the distance…