Related papers: Isoperimetric equalities for rosettes
We study deformations of plane curves in the similarity geometry. It is known that continuous deformations of smooth curves are described by the Burgers hierarchy. In this paper, we formulate the discrete deformation of discrete plane…
We study curve singularities in a smooth surface relative to a smooth boundary curve. We consider the semiuniversal deformations and equisingular deformations of curves with a fixed local intersection number $w$ with the boundary, and prove…
The manuscript is devoted to the boundary behavior of mappings with bounded and finite distortion, which has been actively studied recently. We consider mappings of domains of the Euclidean space that satisfy the inverse Poletsky inequality…
Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
We introduce a new definition of nonpositive curvature in metric spaces and study its relationship to the existing notions of nonpositive curvature in comparison geometry. The main feature of our definition is that it applies to all metric…
In this paper, we study the rigidity of uniform Roe algebras via the ideal structures. We showed that for given metric spaces X and Y with bounded geometry, if their uniform Roe algebras are isomorphic, then they are coarse equivalent.
We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…
Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical semi-symmetric non-metric connection determined by a vector field $\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional curvature with respect to…
The classical uniformization theorem states that any simply connected Riemann surface is conformally equivalent to the disk, the plane, or the sphere, each equipped with a standard conformal structure. We give a similar uniformization for…
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…
In this paper we first prove some linear isoperimetric inequalities for submanifolds in the de Sitter-Schwarzschild and Reissner-Nordstrom manifolds. Moreover, the equality is attained. Next, we prove some monotonicity formulas for…
The Centre Symmetry Set of a planar curve $M$ is the envelope of affine chords of $M$, i.e. the lines joining points on $M$ with parallel tangent lines. In this paper we study global geometrical properties of this set including the number…
A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are…
We prove that the isoperimetric inequalities in the euclidean and hyperbolic plane hold for all euclidean, respectively hyperbolic, cone-metrics on a disk with singularities of negative curvature. This is a discrete analog of the theorems…
This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some…
Many compliant shell mechanisms are periodically corrugated or creased. Being thin, their preferred deformation modes are inextensional, i.e., isometric. Here, we report on a recent characterization of the isometric deformations of periodic…
In this paper, we introduce isophote curves on surfaces in Galilean 3-space. Apart from the general concept of isophotes, we split our studies into two cases to get the axis d of isophote curves lying on a surface such that d is an…
We study reparametrization invariant Sobolev metrics on spaces of regular curves. We discuss their completeness properties and the resulting usability for applications in shape analysis. In particular, we will argue, that the development of…
It was proved by Almgren that among boundaries whose mean curvature is bounded from above, perimeter is uniquely minimized by balls. We obtain sharp stability estimates for Almgren's isoperimetric principle and, as an application, we deduce…