Torsional Rigidity and Bergman Analytic Content of Simply Connected Regions

Tiling simply connected regions with rectangles

Abstract. In 1995, Beauquier, Nivat, Rémila, and Robson showed that tiling of general regions with two rectangles is NP-complete, except for a few trivial special cases. In a different direction, in 2005, Rémila showed that for simply connected regions by two rectangles, the tileability can be solved in quadratic time (in the area). We prove that there is a finite set of at most 10 rectangles f...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

Some results of semilocally simply connected property

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

Isospectral simply-connected homogeneous spaces and the spectral rigidity of group actions

We generalize Sunada’s method to produce new examples of closed, locally non-isometric manifolds which are isospectral. In particular, we produce pairs of isospectral, simplyconnected, locally non-isometric normal homogeneous spaces. These pairs also allow us to see that in general group actions with discrete spectra are not determined up to measurable conjugacy by their spectra. In particular,...

on some properties of analytic spaces connected with bergman metric ball