O teorema da massa positiva e a conjectura de Min-Oo para hiperfícies

Abstract

In this dissertation we study the Positive Mass Theorem and Conjecture Min-Oo for hipersurfaces immersed in R^{n}. The Positive Mass Theorem is a remarkable result in the Geometric Analysis, which remains open for varieties not spin high dimensions also has strong relevance in physics by relating concepts like gravity, mass and total energy of a system. Specifically we find consequences and applications of this theorem in the theory of relativity of Einstein. In this dissertation we present a version of the Positive Mass Theorem for R^{n}. On the other hand, today we know that the Min-Oos Conjecture original is not valid for any variety. In 2011 Brendler, Marques and Neves presented a counterexample to the result, however, we can find several particular cases the result is verified. One of these results is the objective of our work and presented in this dissertation.