In this paper, based on research on rank-one isometries by W. Ballmann and M. Brin and recent research on rank-one isometries of Coxeter groups by P. Caprace and K. Fujiwara, we study a topological fractal structure of boundaries of Coxeter groups. We also show that the limit-point set is dense in a boundary of a Coxeter group and introduce some observations on boundaries of CAT(0) groups with rank-one isometries.

We study the topology of p-harmonic maps ϕ : M →S^ν from a compact Riemannian manifold M into a sphere S^ν. We also show that any p-energy minimizing map ϕ : M → S^ν omitting a totally geodesic submanifold of codimension two Ε S^ν is of class C¹. This extends results by B. Solomon, [13], from harmonic to p-harmonic maps.

In terms of General Topology, we consider ordered additive groups having the order topology, including ordered fields. Namely, we investigate metrizability of these groups or fields, and topological properties of ordered fields in terms of Archimedes' axiom or the axiom of continuity. Also, we give a negative answer to a question in [9]. Finally, we revise the proof of [2, Theorem 2.6], and give some related results.

In this paper we give some results on some abstract second order differential elliptic equations with mixed type boundary conditions. The study is performed in UMD spaces. The main purpose of this paper is the study of necessary and sufficient conditions on the data for obtaining existence, uniqueness and maximal regulariy properties of the strict solution. On the other hand, we give some new examples related to traces results.

This note gives generalizations of Shelah's omitting types theorem and Lopez-Escobar's Theorem.

We discuss the necessary and sufficient conditions for the existence of Lorentzian stationary surfaces in 4-dimensional space forms of index 2, and isometric stationary deformations preserving normal curvature.

In this paper, we give the second limit formula and an analogue of the Chowla-Selberg formula for the twisted Epstein zeta functions of rank n > 2. As an application, we compute the determinant of the Euclidean Laplacian on the space of asymmetrically automorphic functions on Rⁿ by using our second limit formula.

Let $\mathscr{F}$ be a minimal foliation of a complete Riemannian manifold (M, g). Assume that the orthogonal distribution to $\mathscr{F}$ is also integrable. We show that if the growth of $\mathscr{F}$ is at most 2 then any Killing field with bounded length preserves the foliation $mathscr{F}$.

We provide intermediate properties for the domains of the fractional powers of an abstract multivalued linear operator A of weak parabolic type. In particular, our results exhibit the special role played by the linear subspace A0, which reduces to {0} if and only if A is single-valued. The behaviour of the singular semigroup generated by A with respect to the domains of the fractional powers is then studied, and applications of this behaviour to questions of maximal time and space regularity for abstract multivalued evolution equations are given. As a concrete case we consider a class of degenerate partial differential evolution equations which may be rewritten in a multivalued evolution form.