Related papers: On John-Type Ellipsoids
We describe a procedure for constructing formal normal forms of holomorphic maps with a hypersurface of fixed points, and we apply it to obtain a complete list of formal normal forms for 2-dimensional holomorphic maps tangential to a curve…
It is proved that the fixed point submonoid and the periodic point submonoid of a trace monoid endomorphism are always finitely generated. Considering the Foata normal form metric on trace monoids and uniformly continuous endomorphisms, a…
If $\phi$ is an analytic selfmap of the disk (not an elliptic automorphism) the Denjoy-Wolff Theorem predicts the existence of a point $p$ with $|p|\leq 1$ such that the iterates $\phi_{n}$ converge to $p$ uniformly on compact subsets of…
The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T-Kannan type mappings on complete cone metric spaces depended on another function.
We present a vectorial formalism to determine the approximate solutions to the problem of a composite body made of $L$ homogeneous, rigidly rotating layers bounded by spheroidal surfaces. The method is based on the 1st-order expansion of…
We consider a self-homeomorphism h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F. With Le Calvez' transverse foliations theory in…
John's inclusion states that a convex body in $\mathbb{R}^d$ can be covered by the $d$-dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-concave functions. As a byproduct of our approach, we establish…
We consider the discrepancy of the integer lattice with respect to the collection of all translated copies of a dilated convex body having a finite number of flat, possibly non-smooth, points in its boundary. We estimate the $L^{p}$ norm of…
A subset of a convex body $B$ containing the origin in a Euclidean space is {\it parkable in $B$} if it can be translated inside $B$ in such a manner that the translate the origin. We provide characterizations of ellipsoids and of centrally…
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…
Flip graphs of non-crossing configurations in the plane are widely studied objects, e.g., flip graph of triangulations, spanning trees, Hamiltonian cycles, and perfect matchings. Typically, it is an easy exercise to prove connectivity of a…
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are…
For an even set of points in the plane, choose a max-sum matching, that is, a perfect matching maximizing the sum of Euclidean distances of its edges. For each edge of the max-sum matching, consider the ellipse with foci at the edge's…
Three-dimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies these are nondegenerate maxima, minima, and…
A point x is a (bow) tie-point of a space X if X setminus {x} can be partitioned into (relatively) clopen sets each with x in its closure. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of betaN setminus N=…
A topologically minimal surface may be isotoped into a normal form with respect to a fixed triangulation. If the intersection with each tetrahedron is simply connected, then the pieces of this normal form are triangles, quadrilaterals, and…
In this paper we investigate fixed-point numbers of endomorphisms on complex tori. Specifically, motivated by the asymptotic perspective that has turned out in recent years to be so fruitful in Algebraic Geometry, we study how the number of…
We extend to arbitrary finite $n$ the notion of immobilization of a convex body $O$ in $R^n$ by a finite set of points $P$ in the boundary of $O$. Because of its importance for this problem, necessary and sufficient conditions are found for…
The illumination conjecture is a classical open problem in convex and discrete geometry, asserting that every compact convex body~$K$ in $\mathbb R^n$ can be illuminated by a set of no more than $2^n$ points. If $K$ has smooth boundary, it…
A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is…