9 citations · 17 across the 10 of their papers we have counts for
10 papers
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…
A canonical embedding of
Francisco Braun, Frederico Xavier
The group of self-biholomorphisms of consists of affine maps if , but in higher dimensions it is a large object that has n…
On the complexity of isometric immersions of hyperbolic spaces in any codimension
Francisco Fontenele, Frederico Xavier
Although the Nash theorem solves the isometric embedding problem, matters are inherently more involved if one is further seeking an embedding that is well-behaved from the standpoi…
Finiteness of prescribed fibers of local biholomorphisms: a geometric approach
Xiaoyang Chen, Frederico Xavier
Let be a Stein manifold of complex dimension at least two, a local biholomorphism, and . In this paper we formulate sufficient cond…
The index of isolated umbilics on surfaces of non-positive curvature
F. Fontenele, F. Xavier
It is shown that if a surface has negative curvature on the complement of a point , then the -valued Poincaré-Hopf index at of…
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…
Birationality of étale morphisms via surgery
Scott Nollet, Laurence R. Taylor, Frederico Xavier
We use a counting argument and surgery theory to show that if is a sufficiently general algebraic hypersurface in , then any local diffeomorphism o…
Holomorphic injectivity and the Hopf map
Scott Nollet, Frederico Xavier
We give sharp conditions on a local biholomorphism which ensure global injectivity. For , such a map is injective if for each complex line $l \sub…