Related papers: A note on subsets of positive reach
We show, by an elementary and explicit construction, that the group of Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of arbitrary dimension.
We determine the probability that a random k-dimensional subspace of Euclidean n-space contains a positive vector.
We construct an isometric embedding of a bounded set in a Euclidean space into the Gromov-Hausdorff space. In particular, we can embed a bounded and connected Riemannian manifold into the Gromov-Hausdorff space by a bilipschitz map.
Our article is a summary of some results for Riemannian manifolds that were obtained in \cite{gpes}-\cite{Pesssubm}. To the best of our knowledge these are the pioneering papers which contain the most general results about frames, Shannon…
The question whether a Riemannian manifold is geodesically connected can be studied from geometrical as well as variational methods, and accurate results can be obtained by using the associated distance and related properties of the…
We report on our recent breakthrough in the costructionfor q>0 of Hermitean and "tractable" differential operators out of the U_qso(N)-covariant differential calculus on the noncommutative manifolds R_q^N (the socalled "quantum Euclidean…
Recent methods in geometric deep learning have introduced various neural networks to operate over data that lie on Riemannian manifolds. Such networks are often necessary to learn well over graphs with a hierarchical structure or to learn…
This short survey reviews some aspects of spaces of positive-definite self-adjoint linear transformations on R^n and on C^n, including the standard Riemannian metric and the relation with the exponential mapping acting on self-adjoint…
This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…
We present a sharp extension of a result of Bourgain on finding configurations of $k+1$ points in general position in measurable subset of $\mathbb{R}^d$ of positive upper density whenever $d\geq k+1$ to all proper $k$-degenerate distance…
We present some constructions that are merely the fruit of combining recent results from two areas of smooth dynamics: nonuniformly hyperbolic systems and elliptic constructions.
The paper studies strictly positive definite kernels on compact Riemannian manifolds. We state new conditions to ensure strict positive definiteness for general kernels and kernels with certain convolutional structure. We also state…
In this note we improve a gap result concerning the range of the mean curvature of complete $CMC$ proper-biharmonic hypersurfaces in unit Euclidean spheres.
We prove the existence of multiple closed geodesics on non-compact cylindrica manifolds.
We solve the Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds under essentially optimal structure conditions, especially with no restrictions to the curvature of the underlying manifold and the second…
A simple construction is given of a class of Euclidean invariant, reflection positive measures on a compactification of the space of distributions. An unusual feature is that the regularizations used are not reflection positive.
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
We study the intersection of the totally positive part of a split semisimple group over the real numbers with a totally positive parabolic subgroup.
We introduce the notion of positivity for a real basic $(1,1)$ class in basic Bott-Chern cohomology group on foliated manifolds, and study the relationship between this positivity and the negativity of transverse holomorphic sectional…
We will remark an extension of a linear functional on subalgebra of algebra of continuous functions on subset of $\mathbb{R}^n$ which preserves positivity.