A mountain pass theorem for actions of compact Lie groups.
A New Approach to the Rigidity of Discrete Group Actions.
A new Lagrangian dynamic reduction in field theory
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.
Connections on infinite dimensional manifolds with corners
Critical point theory with symmetries.
Division property of the momentum map.
Estimates for critical groups of solutions to quasilinear elliptic systems.
Estudio de las variedades de contacto compactas que admiten una acción foliante.
Harmonic maps into singular spaces and -adic superrigidity for lattices in groups of rank one
Integrable systems and group actions
The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.
Perturbation theorems on Morse theory for continuous functions.
Right closing almost conjugacy for G-shifts of finite type
A G-shift of finite type (G-SFT) is a shift of finite type which commutes with the continuous action of a finite group G. For irreducible G-SFTs we classify right closing almost conjugacy, answering a question of Bill Parry.
Rigidity of Furstenberg entropy for semisimple Lie group actions
Rigidity of group actions
Symmetry groups and Lagrangians associated with Tzitzeica surfaces.
The Tzitzeica surface as solution of PDE systems.
Theory of coverings in the study of Riemann surfaces
For a G-covering Y → Y/G = X induced by a properly discontinuous action of a group G on a topological space Y, there is a natural action of π(X,x) on the set F of points in Y with nontrivial stabilizers in G. We study the covering of X obtained from the universal covering of X and the left action of π(X,x) on F. We find a formula for the number of fixed points of an element g ∈ G which is a generalization of Macbeath's formula applied to an automorphism of a Riemann surface. We give a new method...
Tzitzeica theory -- opportunity for reflection in mathematics.