Related papers: Nonembedding and nonextension results in special h…
We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of…
Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
We consider embedded hypersurfaces evolving by fully nonlinear flows in which the normal speed of motion is a homogeneous degree one, concave or convex function of the principal curvatures, and prove a non-collapsing estimate: Precisely,…
In this paper we discuss the smoothness conditions for metrics on a cohomogeneity one manifold, i.e. metrics invariant under a Lie group whose generic orbits are hypersurfaces. Along these hypersurfaces one describes the metrics in terms of…
Amorphous glassy materials of diverse nature -- concentrated emulsions, granular materials, pastes, molecular glasses -- display complex flow properties, intermediate between solid and liquid, which are at the root of their use in many…
We define new differential structures on the Wasserstein spaces $\mathcal{W}_p(M)$ for $p > 2$ and a general Riemannian manifold $(M,g)$. We consider a very general and possibly degenerate second order partial differential flow equation…
The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make…
We construct Riemannian manifolds with completely integrable geodesic flows, in particular various nonhomogeneous examples. The methods employed are a modification of Thimm's method, Riemannian submersions and connected sums.
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
A variant of the Gauss curvature flow for closed and convex hypersurfaces is considered. We reveal that if the initial hypersurface is pinched enough, then this property is preserved. Furthermore, based on some structure assumptions on the…
To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density…
Recently a new no-global-recollapse argument was given for some inhomogeneous and anisotropic cosmologies that utilizes surface deformation by the mean curvature flow. In this paper we discuss important properties of the mean curvature flow…
We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the…
We consider the hydrodynamics of supersymmetric fluids. Supersymmetry is broken spontaneously and the low energy spectrum includes a fermionic massless mode, the $\mathit{phonino}$. We use two complementary approaches to describe the…
Ambient prime geodesic theorems provide an asymptotic count of closed geodesics by their length and holonomy and imply effective equidistribution of holonomy. We show that for a smoothed count of closed geodesics on compact hyperbolic…
An external description for nonperiodically sampled multivariable linear systems has been developed. Emphasis is on the sampling period sequence, included among the variables to be handled. The computational procedure is simple and no use…
We are interested in the impact of entropies on the geometry of a hypersurface of a Riemannian manifold. In fact, we will be able to compare the volume entropy of a hypersurface with that of the ambient manifold, provided some geometric…
We study the geometry of a codimension-one foliation with a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the Riemannian metric varies along the leaves of the foliation.…
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…