Sobolev Critical Exponents of Rational Homotopy Groups

Rational Homotopy Groups of Generalised Symmetric Spaces

We obtain explicit formulas for the rational homotopy groups of generalised symmetric spaces, i.e., the homogeneous spaces for which the isotropy subgroup appears as the fixed point group of some finite order automorphism of the group. In particular, this gives explicit formulas for the rational homotopy groups of all classical compact symmetric spaces.

Nodal Solutions of Elliptic Equations with Critical Sobolev Exponents

Rational homotopy groups and Koszul algebras

Let X and Y be finite-type CW-spaces (X connected, Y simply connected), such that the ring H∗(Y,Q) is a k-rescaling of H∗(X,Q). If H∗(X,Q) is a Koszul algebra, then the graded Lie algebra π∗(ΩY )⊗Q is the k-rescaling of gr∗(π1X)⊗Q. If Y is a formal space, then the converse holds, and Y is coformal. Furthermore, if X is formal, with Koszul cohomology algebra, there exist filtered group isomorphi...

Critical Exponents for Groups of Isometries

Let Γ be a convex co-compact group of isometries of a CAT(−1) space X and let Γ0 be a normal subgroup of Γ. We show that, provided Γ is a free group, a sufficient condition for Γ and Γ0 to have the same critical exponent is that Γ/Γ0 is amenable. 0. Introduction and Results Let Γ be a group of isometries acting freely and properly discontinuously on a CAT(−1) space X . Roughly speaking, a CAT(−...

A Nonlinear Elliptic PDE with Two Sobolev-Hardy Critical Exponents

In this paper, we consider the following PDE involving two Sobolev-Hardy critical exponents,