Manifolds close to the round sphere
Marenich, Valery
Illinois J. Math., Tome 45 (2001) no. 4, p. 615-629 / Harvested from Project Euclid
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We prove that the manifold $M^n$ of minimal radial curvature $K^{\min}_o\geq 1$ is homeomorphic to the sphere $S^n$ if its radius or volume is larger than half the radius or volume of the round sphere of constant curvature $1$. These results are optimal and give a complete generalization of the corresponding results for manifolds of sectional curvature bounded from below.
Publié le : 2001-04-15
Classification:  53C20,  53C21 
@article{1258138359,
     author = {Marenich, Valery},
     title = {Manifolds close to the round sphere},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 615-629},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138359}
}

Marenich, Valery. Manifolds close to the round sphere. Illinois J. Math., Tome 45 (2001) no. 4, pp.  615-629. http://gdmltest.u-ga.fr/item/1258138359/