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math.AP2020
Functional Inequalities involving Nonlocal Operators on Complete Riemannian Manifolds and Their Applications to The Fractional Porous Medium Equation
Nikolaos Roidos, Yuanzhen Shao
The objective of this paper is twofold. First, we conduct a careful study of various functional inequalities involving the fractional Laplacian operators, including nonlocal Sobole…
math.DG2020
Curve shortening flow on Riemann surfaces with conical singularities
Nikolaos Roidos, Andreas Savas-Halilaj
We study the curve shortening flow on Riemann surfaces with finitely many conformal conical singularities. If the initial curve is passing through the singular points, then the evo…