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math.DG2013
Sobolev and isoperimetric inequalities for submanifolds in weighted ambient spaces
Marcio Batista, Heudson Mirandola
In this paper, we prove a Sobolev and isoperimetric inequalities for submanifold in weighted manifold. Our results generalize the Hoffman-Spruck's inequalities.
math.DG2013
The positive mass Theorem and Penrose inequality for graphical manifolds
Heudson Mirandola, Feliciano Vitorio
We give, via elementary methods, explicit formulas for the ADM mass which allow us to conclude the positive mass theorem and Penrose inequality for a class of graphical manifolds w…