Optimal rigidity estimates for nearly umbilical surfaces in arbitrary codimension

A C Estimate for Nearly Umbilical Surfaces

An incremental algorithm for reconstruction of surfaces of arbitrary codimension

A new algorithm is presented for surface reconstruction from unorganized points. Unlike many previous algorithms, this algorithm does not select a subcomplex of the Delaunay Triangulation of the points. Instead, it uses an incremental algorithm, adding one simplex of the surface at a time. As a result, the algorithm does not require the surface’s embedding space to be R3; the dimension of the e...

Isometric rigidity in codimension two

In the local theory of submanifolds a fundamental but difficult problem is to describe the isometrically deformable isometric immersions f : M → R into Euclidean space with low codimension p if compared to the dimension n ≥ 3 of the Riemannian manifold. Moreover, one would like to understand the set of all possible isometric deformations. Submanifolds in low codimension are generically rigid si...

HÖLDER AND L ESTIMATES FOR b ON CR MANIFOLDS OF ARBITRARY CODIMENSION

The ∂̄b complex on the boundary of a complex manifold was first formulated by Kohn-Rossi [KR] to study the boundary values of holomorphic functions and holomorphic extensions. In this paper we study ∂̄b and b on a CR manifold of arbitrary codimension. When the CR manifold M is of codimension 1 and strongly pseudoconvex (or more generally, when M satisfies condition Y (q)), Kohn [K2] proved that b...

Slant surfaces of codimension two

A slant immersion is an isometric immersion from a Riemannian manifold into an almost Hermitian manifold with constant Wirtinger angle (1~ . In this article we study and characterize slant surfaces in the complex 2-plane ~2 via the Gauss map. We also prove that every surface without complex tangent points in a 4-dimensional almost Hermitian manifold M is slant with respect to a suitably chosen ...