A Cantor set in the unit sphere in ℂ2 with large polynomial hull

Linear Weingarten hypersurfaces in a unit sphere

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

Polynomial Interpolation on the Unit Sphere

Polynomial interpolation on the unit sphere II

The problem of interpolation at (n+1) points on the unit sphere S by spherical polynomials of degree at most n is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials.

Maximizing a Second-degree Polynomial on the Unit Sphere

Let A be a hermitian matrix of order n, and b a known vector in n C . The problem is to determine which vectors make 0(x) = (x-b)H A(x-b) a maximum or minimum on the unit sphere U = [x H : xx= 13 l The problem is reduced to the determination of a finite point set, the spectrum of (A,b). The theory reduces to the usual theory of hermitian forms when b = 0. 1* Reproduction in Whole or in Part is ...

A classification of hull operators in archimedean lattice-ordered groups with unit

The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...