Affine complete locally convex hypersurfaces

2002 ◽  
Vol 150 (1) ◽  
pp. 45-60 ◽  
Author(s):  
Neil S. Trudinger ◽  
Xu-Jia Wang
Keyword(s):  
Affine Complete ◽  
Locally Convex ◽  
Convex Hypersurfaces

Locally Convex Hypersurfaces

1973 ◽  
Vol 25 (3) ◽  
pp. 531-538 ◽  
Author(s):  
L. B. Jonker ◽  
R. D. Norman
Keyword(s):  
Convex Body ◽  
Open Subset ◽  
Convex Hypersurface ◽  
Topological Manifold ◽  
Continuous Map ◽  
Open Set ◽  
Locally Convex ◽  
Convex Hypersurfaces

Let M be an n-dimensional connected topological manifold. Let ξ : M → Rn+1 be a continuous map with the following property: to each x ∈ M there is an open set x ∈ Ux ⊂ M, and a convex body Kx ⊂ Rn+1 such that ξ(UX) is an open subset of ∂Kx and such that is a homeomorphism onto its image. We shall call such a mapping ξ a locally convex immersion and, along with Van Heijenoort [8] we shall call ξ(M) a locally convex hypersurface of Rn+1.

Locally convex hypersurfaces immersed in $$\mathbb {H}^n\times \mathbb {R}$$ H n × R

2016 ◽  
Vol 188 (1) ◽  
pp. 17-32 ◽  
Author(s):  
Inês S. de Oliveira Padilha ◽  
S. J. Paul A. Schweitzer
Keyword(s):  
Locally Convex ◽  
Convex Hypersurfaces
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