Search results for "geometry and topology"

Convexly generic curves in R 3

1988

We study curves immersed in R 3, with special interest in the description of their convex hull frontier structure from a global viewpoint. Genericity conditions are set for these curves by looking at the singularities of height functions on them. We define panel structures for convexly generic curves and work out numerical relations involving the number of tritangent support planes. As a consequence, a generic version of the 4-vertex theorem for convex curves in R 3 is obtained.

Heat Kernel Measure on Central Extension of Current Groups in any Dimension

2006

We define measures on central extension of current groups in any dimension by using infinite dimensional Brownian motion.

Mappings of finite distortion: Formation of cusps II

2007

For s > 0 s>0 given, we consider a planar domain  Ω s \Omega _s with a rectifiable boundary but containing a cusp of degree  s s , and show that there is no homeomorphism f : R 2 → R 2 f\colon \mathbb {R}^2\to \mathbb {R}^2 of finite distortion with exp ⁡ ( λ K ) ∈ L l o c 1 ( R 2 ) \exp (\lambda K)\in L^1_{\mathrm {loc}}(\mathbb {R}^2) so that f ( B ) = Ω s f(B)=\Omega _s when λ > 4 / s \lambda >4/s and  B B is the unit disc. On the other hand, for λ > 2 / s \lambda >2/s such an  f f exists. The critical value for λ \lambda remains open.

A note to “Mappings of finite distortion: formation of cusps II”

2010

We consider planar homeomorphisms f : R 2 → R 2 f\colon \mathbb {R}^2\to \mathbb {R}^2 that are of finite distortion and map the unit disk onto a specific cusp domain  Ω s \Omega _s . We study the relation between the degree  s s of the cusp and the integrability of the distortion function  K f K_f by sharpening a previous result where  K f K_f is assumed to be locally exponentially integrable.

A Dido problem for domains in ?2 with a given inradius

1990

We find which are the simply connected domains in ℝ2 satisfying the Dido condition for a straight shoreline, with a given area A and a fixed inradius ϱ, which minimize the length of the free boundary. There are three different cases according to the values of A and ϱ.

Quasi-Newton approach to nonnegative image restorations

2000

Abstract Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform (FFT) based schemes result in efficient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an image consists of positive light intensities, and thus a nonnegativity constraint should be enforced. This constraint and other ways of incorporating a priori information have been suggested in various applications, and can lead to substantial improvements in the reconstructions. Neverth…

Boundary behavior of quasi-regular maps and the isodiametric profile

2001

We study obstructions for a quasi-regular mapping f : M → N f:M\rightarrow N of finite degree between Riemannian manifolds to blow up on or collapse on a non-trivial part of the boundary of M M .

A note on rank 2 diagonals

2020

<p>We solve two questions regarding spaces with a (G<sub>δ</sub>)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos about weakly Lindelöf spaces with a G<sub>δ</sub>-diagonal of rank 2 and the other is a question of Arhangel’skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.</p>

Volumes of certain small geodesic balls and almost-Hermitian geometry

1984

Let D be the characteristic connection of an almost-Hermitian manifold, V D m (r) the volume of a small geodesic ball for the connection D and C C D 1 the first non-trivial term of the Taylor expansion of V D m (r). NK-manifolds are characterized in terms of C C D 1 and a family of Hermitian manifolds for which ∫ M C C D 1 dvol is a spectral invariant is given and one proves that C C D 1 and the spectrum of the complex Laplacian, together, determine the class in which a compact Hermitian manifold lines.

On a-semiaffine planes with invisible lines

1987