Bishop-Gromovs theorem of comparison of volume. / O Teorema de Comparação de Volume de Bishop-Gromov.
AUTOR(ES)
Erikson Alexandre Fonseca dos Santos
DATA DE PUBLICAÇÃO
2009
RESUMO
IN THIS dissertation, we use the Laplacian comparison theorem to prove the comparison of volume Bishop-Gromovs theorem, which assures that if the Ricci curvatures of a complete Riemannian manifold are larger than or equal to (n - 1)k, the volume of a ball with center in p and radius R is smaller than or equal to the volume of a geodesic ball with radius R in the space form of sectional constant curvature k, for all p 2 M and R >0, where k 2 R. Moreover, equality occurs if all sectional curvature throughout geodesics connecting p and x, for plans which contain the radial vector, is constant and equal to k.
ASSUNTO(S)
matematica volume of an open and connected region weitzenböcks formula laplacian comparison theorem teorema de comparação de volume de bishop-gromov comparison of volume bishop-gromovs theorem volume de uma região aberta e conexa teorema de comparação do laplaciano fórmula de weitzenböck
