Related papers: Parseval space-frequency localized frames on sub-R…
We describe a setting for homogenization of convex hamiltonians on abelian covers of any compact manifold. In this context we also provide a simple variational proof of standard homogenization results.
We establish a broad notion of admissible tilings of frequency space which admit associated wave packet frames with elements which are smooth and compactly supported. The framework is designed to allow for tile geometries which are…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
In this article, we study compactifications of homogeneous spaces coming from equivariant, open embeddings into a generalized flag manifold $G/P$. The key to this approach is that in each case $G/P$ is the homogeneous model for a parabolic…
We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to the real axis. We…
On the Grassmann manifold G (m, n) of m-dimensional subspaces of an n-dimensional projective space P^n, a certain supplementary construction called the normalization is considered. By means of this normalization, one can construct the…
On a compact manifold with boundary, the map consisting of the scalar curvature in the interior and the mean curvature on the boundary is a local surjection at generic metrics. We prove that this result may be localized to compact…
In this paper we construct compact manifolds with fixed boundary geometry which admit Riemannian metrics of unit volume with arbitrarily large Steklov spectral gap. We also study the effect of localized conformal deformations that fix the…
The $n$-dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the $(n+1)$-dimensional complex projective space, which is isometric to the real Grassmann manifold of oriented 2-…
We extend the recent result of T.Tao to wave maps defined from the Minkowski space of dimension >4 to a target Riemannian manifold which possesses a ``bounded parallelizable'' structure. This is the case of Lie groups, homogeneous spaces as…
This paper reports the design of a high-accuracy spatial location estimation method using ultrasound waves by exploiting the fixed geometry of the transmitters. Assuming an isosceles triangle antenna configuration, where three antennas are…
We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality…
Inspired by recent interest in geometric deep learning, this work generalises the recently developed Slepian scale-discretised wavelets on the sphere to Riemannian manifolds. Through the sifting convolution, one may define translations and,…
We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey…
We classify all proper-biharmonic Legendre curves in a Sasakian space form and point out some of their geometric properties. Then we provide a method for constructing anti-invariant proper-biharmonic submanifolds in Sasakian space forms.…
We study Sobolev spaces of radial functions on spherically symmetric Riemannian manifolds. Using geodesic polar coordinates, we give a sharp one-dimensional reduction: a radial function belongs to the Sobolev space on the manifold if and…
This note concerns the topology of the connected components of the zero sets of monochromatic random waves on compact Riemannian manifolds without boundary. In [SW] it is shown that these are distributed according to a universal measure on…
In this paper, we introduce the notion of a quasi-biharmonic submanifold in a pseudo-Riemannian manifold and classify quasi-biharmonic marginally trapped Lagrangian surfaces in Lorentzian complex space forms.
In this article, we investigate sequences of discontinuous martingales on submanifolds of higher-dimensional Euclidean space. Those sequences naturally arise when we deal with a sequence of harmonic maps with respect to non-local Dirichlet…
The purpose of this note is to show that a connection with closed skewsymmetric torsion and reducible holonomy admits a locally defined Riemannian submersion together with a projected geometry on the base. We reframe known submersion…