Related papers: Higher dimensional Jordan curves
We show how inscription problems in the plane can be generalized to Riemannian surfaces of constant curvature. We then use ideas from symplectic and Riemannian geometry to prove these generalized versions for smooth Jordan curves in the…
We study capability of $f(R)$ gravity models to allow crossing the phantom boundary in both Jordan and Einstein conformal frames. In Einstein frame, these models are equivalent to Einstein gravity together with a scalar field minimally…
Assume you are given a finite configuration $\Gamma$ of disjoint rectifiable Jordan curves in $\mathbb{R}^n$. The Plateau-Douglas problem asks whether there exists a minimizer of area among all compact surfaces of genus at most $p$ which…
We discuss possible observational manifestations of static, spherically symmetric solutions of a class of multidimensional theories of gravity, which includes the low energy limits of supergravities and superstring theories as special…
We prove the existence of a Hermitian-Einstein metric on holomorphic vector bundles with a Hermitian metric satisfying the analytic stability condition, under some assumption for the underlying K\"ahler manifolds. We also study the…
For every smooth Jordan curve $\gamma$ and cyclic quadrilateral $Q$ in the Euclidean plane, we show that there exists an orientation-preserving similarity taking the vertices of $Q$ to $\gamma$. The proof relies on the theorem of…
Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently…
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 use homotopy theory to extend the notion of strong and weak topological insulators to the non-stable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly…
We study non-perturbative quantization of 3d gravity with positive cosmological constant (de Sitter space being the prototype vacuum solution, whose Euclideanization of course gives the three sphere) on the background topology of lens…
Jordan geometries are defined as spaces equipped with point reflections depending on triples of points, exchanging two of the points and fixing the third. In a similar way, symmetric spaces have been defined by Loos (Symmetric Spaces I,…
Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general…
We study the set $R$ of nonplanar rational curves of degree $d<q+2$ on a smooth Hermitian surface $X$ of degree $q+1$ defined over an algebraically closed field of characteristic $p>0$, where $q$ is a power of $p$. We prove that $R$ is the…
In this paper we prove some rigidity theorems associated to $Q$-curvature analysis on asymptotically Euclidean (AE) manifolds, which are inspired by the analysis of conservation principles within fourth order gravitational theories. A…
We exhibit a closed hyperbolic 3-manifold which satisfies a very strong form of Thurston's Virtual Fibration Conjecture. In particular, this manifold has finite covers which fiber over the circle in arbitrarily many ways. More precisely, it…
We show that the homology of the Jones annular algebras is isomorphic to that of the cyclic groups below a line of gradient $\frac{1}{2}$. We also show that the homology of the partition algebras is isomorphic to that of the symmetric…
Ueda's theory is a theory on a flatness criterion around a smooth hypersurface of a certain type of topologically trivial holomorphic line bundles. We propose a codimension two analogue of Ueda's theory. As an application, we give a…
We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all…
In this paper we study some aspects of curved BPS-like domain walls in higher dimensional gravity theory coupled to scalars where the scalars span a complex K\"ahler surface with scalar potential turned on. Assuming that a fake…
We show that various loci of stable curves of sufficiently large genus admitting degree $d$ covers of positive genus curves define non-tautological algebraic cycles on $\overline{\mathcal{M}}_{g,N}$, assuming the non-vanishing of the $d$-th…