When 2−1/Q<p≤2, we establish the Cloc0,1 and Cloc1,α-regularities of weak solutions to quasi-linear p-Laplacian type non-homogeneous equations in Heisenberg group Hn, where Q=2n+2 is homogeneous dimension Hn.

In several areas of mathematics, homogeneous spaces are fundamental objects as they often serve as models for more general objects: Various examples from differential geometry (Riemannian symmetric spaces, principal bundles) and topology (geometric 3-manifolds), to algebraic and complex geometry (uniformization theorems, flag manifolds) etc. underline the importance of spaces, furnished with a ...

In this note we give a structure theorem for a finite-dimensional subgroup of the automorphism group of a compact symplectic manifold. An application of this result is a simpler and more transparent proof of the classification of compact homogeneous spaces with invariant symplectic structures. We also give another proof of the classification from the general theory of compact homogeneous spaces...

We show that locally connected, simply connected homogeneous continua are not separated by arcs. We ask several questions about homogeneous continua which are inspired by analogous questions in geometric group theory.

Homogeneous solutions to topologically massive gravity have been previously found for spacetimes in 2+1 dimensions admitting a simply transitive isometry group. We discuss the case of homogeneous spacetimes in 2+1 dimensions with isotropy, review a technique for classifying them, and examine in each case whether the isometry group has a simply transitive subgroup. We further show that none of t...

The study of reductive group actions on a normal surface singularity X is facilitated by the fact that the group AutX of automorphisms of X has a maximal reductive algebraic subgroup G which contains every reductive algebraic subgroup of AutX up to conjugation. If X is not weighted homogeneous then this maximal group G is finite (Scheja, Wiebe). It has been determined for cusp singularities by ...