A Neumann problem with the -Laplacian on a solid torus in the critical of supercritical case.
A New Approach to the Rigidity of Discrete Group Actions.
Affine Actions of Higher Rank Lattices.
Determination of the topological structure of an orbifold by its group of orbifold diffeomorphisms.
Equivariant maps of joins of finite G-sets and an application to critical point theory
A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function , where G is a finite nontrivial group acting freely and orthogonally on . Neither Morse theory nor the minimax method is applied. The proofs are based on a general version of Borsuk’s Antipodal Theorem for equivariant maps of joins of G-sets.
Generic simplicity of eigenvalues for a Dirichlet problem of the bilaplacian operator.
Geodesic reduction via frame bundle geometry.
Geometry of compactifications of locally symmetric spaces
For a locally symmetric space , we define a compactification which we call the “geodesic compactification”. It is constructed by adding limit points in to certain geodesics in . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give for locally symmetric spaces. Moreover, has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...
Holonomy orbits of the snake charmer algorithm
Large group actions on manifolds.
On -sets and isospectrality
We study finite -sets and their tensor product with Riemannian manifolds, and obtain results on isospectral quotients and covers. In particular, we show the following: If is a compact connected Riemannian manifold (or orbifold) whose fundamental group has a finite non-cyclic quotient, then has isospectral non-isometric covers.
On rank one symmetric space
In this paper we survey some recent results on rank one symmetric space.
On self-dual pseudo-connections on some orbifolds.
On symmetrically growing bodies.
This work presents a setting for the formulation of the mechanics of growing bodies. By the mechanics of growing bodies we mean a theory in which the material structure of the body does not remain fixed. Material points may be added or removed from the body.
On the uniqueness of the analyticity of a proper G-action.
Permutations; isotropy and smooth cyclic group actions on definite 4-manifolds.
Representation of a gauge group as motions of a Hilbert space
This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject.In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered as a Lie group. The second...
Rigidity of group actions
Symmetries and integration of differential equations.
Variational principles for differential equations with symmetries and conservation laws. II. Polynomial differential equations.