Critical phenomena in gravitational collapse
A mini-introduction to critical phenomena in gravitational collapse is combined with a more detailed discussion of how gravity regularizes the 'critical spacetimes' that dominate these phenomena.
Curl bounds grad on SO(3)
Let be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form applied to rotations controls the gradient in the sense that pointwise . This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math. 55 (2002) 1461–1506; John, Comme Pure Appl. Math. 14 (1961) 391–413; Reshetnyak, Siberian Math. J. 8 (1967) 631–653)] as well as an associated linearized theorem...
Curl bounds Grad on SO(3)
Let be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form applied to rotations controls the gradient in the sense that pointwise . This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math.55 (2002) 1461–1506; John, Comme Pure Appl. Math.14 (1961) 391–413; Reshetnyak, Siberian Math. J.8 (1967) 631–653)] as well as an associated linearized theorem saying...
Decay estimates for spherically symmetric Yang-Mills fields in Minkowski space-time
Editors’ preface for the topical issue “Finite dimensional integrable systems, dynamics, and Lie theoretic methods in Geometry and Mathematical Physics”
Eigenvalues of Killing tensors and separable webs on Riemannian and pseudo-Riemannian manifolds.
Einstein gravity, Lagrange-Finsler geometry, and nonsymmetric metrics.
Electromagnetic dynamical systems.
Erratum: J. Eur. Math. Soc. 1, 237-311 (1999)
Fastest curves and toroidal black holes
We discuss an apparent paradox (and conjectured resolution) of Jacobson and Venkataramani concerning 'temporarily toroidal' black hole horizons, in light of a recent connectivity theorem for spaces of complete causal curves. We do this in a self-contained manner by first reviewing the 'fastest curve argument' which proves this connectivity theorem, and we note that active topological censorship can be derived as a corollary of this argument. We argue that the apparent paradox arises only when one...
Finsler cases of GF-space.
Generalized Hasimoto transform of one-dimensional dispersive flows into compact Riemann surfaces.
Generalized PN manifolds and separation of variables
The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.
Geometric modular action and transformation groups
Geometric physics.
Global dynamics of media with microstructure.
Gravitational scattering of electromagnetic field by Schwarzschild black-hole
Hidden symmetries of -theory and its dynamical realization.
Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
Huygens' principle on Petrov type N space-times