相关论文: Ahlfors-Regular Curves In Metric Spaces

In this work, the dual flatness, which is connected with Statistics and Information geometry, of general $(\alpha,\beta)$-metrics (a new class of Finsler metrics) is studied. A nice characterization for such metrics to be dually flat under…

We consider the curves whose all normal planes are at the same distance from a fixed point and obtain some characterizations of them in the 3-dimensional Euclidean space.

We study the motion of sets by anisotropic curvature under a volume constraint in the plane. We establish the exponential convergence of the area-preserving anisotropic flat flow to a disjoint union of Wulff shapes of equal area, the…

We define a generalization of the fixed point set, called the bounded fixed set, for a group acting by isometries on a metric space. An analogue of the P. A. Smith theorem is proved for metric spaces of finite asymptotic dimension, which…

Generalized (rational) graph contractions in the framework of a dislocated metric space endowed with a directed graph are investigated. Fixed point results for set-contractions are obtained. We also provide some examples to illustrate our…

The aim of this paper is to verify that the study of generic conformally flat hypersurfaces in 4-dimensional space forms is reduced to a surface theory in the standard 3-sphere. The conformal structure of generic conformally flat…

The main purpose of the note is to explore the invariant properties of sphericalization and flattening and their applications in quasi-metric spaces. We show that sphericalization and flattening procedures on a quasimetric spaces preserving…

To any metric spaces there is an associated metric profile. The rectifiability of the metric profile gives a good notion of curvature of a sub-Riemannian space. We shall say that a curvature class is the rectifiability class of the metric…

As first noted in Korevaar, Kusner and Solomon ("KKS"), constant mean curvature implies a homological conservation law for hypersurfaces in ambient spaces with Killing fields.In Theorem 3.5 here, we generalize that law by relaxing the…

An area metric is a (0,4)-tensor with certain symmetries on a 4-manifold that represent a non-dissipative linear electromagnetic medium. A recent result by Schuller, Witte and Wohlfarth provides a pointwise normal form theorem for such area…

We construct examples of compact and one-ended constant mean curvature surfaces with large mean curvature in Riemannian manifolds with axial symmetry by gluing together small spheres positioned end-to-end along a geodesic. Such surfaces…

This paper, the second of a series, deals with the function space of all smooth K\"ahler metrics in any given closed complex manifold $M$ in a fixed cohomology class. The previous result of the second author \cite{chen991} showed that the…

We study the generalized roundness of finite metric spaces whose distance matrix $D$ has the property that every row of $D$ is a permutation of the first row. The analysis provides a way to characterize subsets of the Hamming cube $\{ 0, 1…

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…

We study the existence problem for achronal hypersurfaces $M \hookrightarrow \overline{M}$ in a globally hyperbolic spacetime, whose mean curvature is a prescribed -- possibly singular -- source, and whose boundary is a given smooth…

We study mean convex mean curvature flow $M_s$ of local spacelike graphs in the flat slicing of de Sitter space. We show that if the initial slice is of non-negative time and is graphical over a large enough ball, and if $M_s$ is of bounded…

The aim of this paper is to study pointed Gromov-Hausdorff Convergence of sequences of K\"ahler submanifolds of a fixed K\"ahler ambient space. Our result shows that lower bounds on the scalar curvature imply convergence to a smooth…

In this paper we study the geometry of metric spheres in the curve complex of a surface, with the goal of determining the "average" distance between points on a given sphere. Averaging is not technically possible because metric spheres in…

In this paper we study flatness of the restriction on some special subgerms (e.g. the reduction and the unmixed part) of the total space of a flat morphism over a smooth base space. We give a relationship between reducedness of the total…

In this paper we study the flag curvature of a particular class of Finsler metrics called general $(\alpha,\beta)$-metrics, which are defined by a Riemannian metric $\alpha$ and a $1$-form $\beta$. The classification of such metrics with…