Related papers: Borsuk-Ulam Type Theorems and Mountain Climbing Pr…

We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.

The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to the 1920s with the theorems of Jarnik and Besicovitch regarding well-approximable and badly-approximable points. In this paper we consider…

We extend the circle of ideas from a previous paper on hypersurfaces to functions $f \colon (\mathbb C^n, 0) \to (\mathbb C^k, 0)$ with an isolated singularity in a stratified sense on an arbitrary, but fixed complex analytic germ $(X, 0)$.…

Let $\pi: E \to B$ be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let $\pi^{'}: E^{'} \to B$ be vector bundle such that $\mathbb{Z}_2$ acts fiber preserving and freely on $E$ and…

Let $M$ be a smooth, compact, connected, oriented Riemannian manifold, and let $\imath: M \to \mathbb R^d$ be an isometric embedding. We show that a Sobolev map $f: M \to M$ which has the property that the differential $df(q)$ is close to…

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

We extend the definition of topological pressure to locally compact Hausdorff spaces, and we demonstrate a "variational principle" comparing the topological and measure theoretic pressures. Given a continuous $\mathbb{Z}_+^N$-action $T$…

In this paper, we introduce the concepts of m-quasiconvex, originally m-quasiconvex,and generalized m-quasiconvex functionals on topological vector spaces. Then we extend the concept of point separable topological vector spaces (by the…

We study a Type IIB isotropic toroidal compactification with non-geometric fluxes. Under the assumption of a hierarchy on the moduli, an effective scalar potential is constructed showing a runaway direction on the real part of the K\"ahler…

Let M and N be topological spaces such that M admits a free involution $\\tau$. A homotopy class $\beta$ $\in$ [M, N ] is said to have the Borsuk-Ulam property with respect to $\\tau$ if for every representative map f : M $\rightarrow$ N of…

Hopf conjectured that even-dimensional closed Riemannian manifolds with positive sectional curvature have positive Euler characteristic. The conclusion of the conjecture is known to fail if the positive sectional curvature assumption is…

We present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin.…

Given a closed connected Riemannian manifold M and a connected Riemannian manifold N, we study fiberwise volume decreasing diffeomorphisms on the product M x N. Our main theorem shows that in the presence of certain cohomological condition…

We prove a new version of isoperimetric inequality: Given a positive real $m$, a Banach space $B$, a closed subset $Y$ of metric space $X$ and a continuous map $f:Y \rightarrow B$ with $f(Y)$ compact $$\inf_FHC_{m+1}(F(X))\leq…

Let $M$ be a topological space that admits a free involution $\tau$, and let $N$ be a topological space. A homotopy class $\beta \in [ M,N ]$ is said to have {\it the Borsuk-Ulam property with respect to $\tau$} if for every representative…

In this paper, we use the thermodynamical formalism to show that there exists a unique equilibrium state $\mu_\phi$ for each expanding Thurston map $f: S^2\rightarrow S^2$ together with a real-valued H\"older continuous potential $\phi$.…

Brehm's extension theorem states that a non-expansive map on a finite subset of a Euclidean space can be extended to a piecewise-linear map on the entire space. In this note, it is verified that the proof of the theorem is constructive…

In this paper, we find that the integrated form $d_F$ of a complex Finsler metric $F$ is inner. The distance $d_F$ is complete if and only if every closed bounded subset of a complex manifold $M$ is compact. We prove a version of theorem…

Suppose that $M$ is a topological monoid satisfying $\pi_0M=\mathbb{N}$ to which the McDuff-Segal group-completion theorem applies. This implies that a certain map $f: \mathbb{M}_{\infty}\rightarrow \Omega BM$ defined on an infinite mapping…

Given any complex Laurent polynomial $f$, $\mathrm{Amoeba}(f)$ is the image of its complex zero set under the coordinate-wise log absolute value map. We give an efficiently constructible polyhedral approximation, $\mathrm{ArchtTrop}(f)$, of…