Convex hypersurfaces.

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Affine complete locally convex hypersurfaces

An open problem in affine geometry is whether an affine complete locally uniformly convex hypersurface in Euclidean (n + 1)-space is Euclidean complete for n ≥ 2. In this paper we give the affirmative answer. As an application, it follows that an affine complete, affine maximal surface in R3 must be an elliptic paraboloid.

متن کامل

Convex hypersurfaces of prescribed curvatures

For a smooth strictly convex closed hypersurface Σ in R, the Gauss map n : Σ → S is a diffeomorphism. A fundamental question in classical differential geometry concerns how much one can recover through the inverse Gauss map when some information is prescribed on S ([27]). This question has attracted much attention for more than a hundred years. The most notable example is probably the Minkowski...

متن کامل

Convex Hypersurfaces with Pinched Principal Curvatures and Flow of Convex Hypersurfaces by High Powers of Curvature

We consider convex hypersurfaces for which the ratio of principal curvatures at each point is bounded by a function of the maximum principal curvature with limit 1 at infinity. We prove that the ratio of circumradius to inradius is bounded by a function of the circumradius with limit 1 at zero. We apply this result to the motion of hypersurfaces by arbitrary speeds which are smooth homogeneous ...

متن کامل

Deformations of Unbounded Convex Bodies and Hypersurfaces

We study the topology of the space ∂K of complete convex hypersurfaces of R which are homeomorphic to Rn−1. In particular, using Minkowski sums, we construct a deformation retraction of ∂K onto the Grassmannian space of hyperplanes. So every hypersurface in ∂K may be flattened in a canonical way. Further, the total curvature of each hypersurface evolves continuously and monotonically under this...

متن کامل

On Locally Convex Hypersurfaces with Boundary

In this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Michigan Mathematical Journal

سال: 1972

ISSN: 0026-2285

DOI: 10.1307/mmj/1029000841