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A conformal characterization of manifolds of constant sectional curvature
Xiaoyang Chen, Francisco Fontenele, Frederico Xavier
A special case of the main result states that a complete -connected Riemannian manifold is isometric to one of the models , , of…
Conformal geometry, Euler numbers, and global invertibility in higher dimensions
Frederico Xavier
It is shown that in dimension at least three a local diffeomorphism of Euclidean n-space into itself is injective provided that the pull-back of every plane is a Riemannian submani…
Good shadows, dynamics, and convex hulls
Francisco Fontenele, Frederico Xavier
The Ekeland variational principle implies what can be regarded as a strong version, in the category, of the Yau minimum principle: under the appropriate hypotheses {\it every…
A Riemannian Bieberbach estimate
Francisco Fontenele, Frederico Xavier
The Bieberbach estimate, a pivotal result in the classical theory of univalent functions, states that any injective holomorphic function on the open unit disc satisfies $|f…