相关论文: The curvature of orbit spaces

We investigate the problem of finding complete strictly convex hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of curvature functions.

We study the possibility to probe the spatial geometry of the Universe by supernova measurement of the cubic correction to the luminosity distance. We illustrate with an accelerating universe model with infinite-volume extra dimensions, for…

We give a survey of various recent developments in orbit equivalence and measured group theory. This subject aims at studying infinite countable groups through their measure preserving actions.

This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group…

The space rotation invariance hypothesis is examined. The basic space-time properties and the physical object description from this point of view are considered. An $\omega$-invariance as an approximation of the space rotation invariance…

Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area-decreasing map…

We consider an addition of the term which is a square of the scalar curvature to the Einstein-Hilbert action. Under this generalized action, we attempt to explain i) the flat rotation curves observed in spiral galaxies, which is usually…

We bound the number of incidences between points and spheres in finite vector spaces by bounding the sum of the number of points in the pairwise intersections of the spheres. We obtain new incidence bounds that are interesting when the…

In this paper we prove that an isometry between orbit spaces of two proper isometric actions is smooth if it preserves the codimension of the orbits or if the orbit spaces have no boundary. In other words, we generalize Myers-Steenrod's…

The geodesic total curvature of rectifiable spherical curves is analyzed. We extend to the case of high dimension spheres the explicit formula that holds true for curves supported into the 2-sphere. For this purpose, we take advantage of…

We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…

We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface. In case that the curve has constant torsion, we obtain the…

The paper 0705.0332v1 seeks to study the effect of non-trivial spatial curvature in homogeneous and isotropic models. We note that the space considered is not homogeneous, and that the equations of motion used are inconsistent with the…

Some boundedness properties of function spaces (considered as topological groups) are studied.

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties…

The aim of this paper is to investigate the equivalence conditions for uniform perfectness of quasi-metric spaces. We also obtain the invariant property of uniform perfectness under quasim\"obius maps in quasi-metric spaces. In the end, two…

We show that every effective action of a compact Lie group $K$ on a unit sphere $S^n$ admits an explicit orbit whose principal curvatures are bounded from above by $4\sqrt{14}$.

Some examples and basic properties of ultrametric spaces are briefly discussed.

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry…