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math.DG2024
Perelman singular manifolds
Márcio Batista, Allan Freitas, Márcio Santos
On a Riemannian manifold with a smooth function , we consider the linearization of the Perelman scalar curvature and its -formal adjoint oper…
math.DG2016
Hardy and Rellich Inequalities for submanifolds in Hadamard spaces
Marcio Batista, Heudson Mirandola, Feliciano Vitorio
Some of the most known integral inequalities are the Sobolev, Hardy and Rellich inequalities in Euclidean spaces. In the context of submanifolds, the Sobolev inequality was proved…
math.DG2012
Integral estimates for the trace of symmetric operators
Marcio Batista, Heudson Mirandola
Let be a positive-semidefinite symmetric operator of class defined on a complete non-compact manifold isometrically immersed in a Hadamard space . I…