Related papers: A sharp stability estimate for tensor tomography i…

In this paper we answer two long-standing questions in the classification of $G$-torsors on curves for an almost simple, simply connected algebraic group $G$ over the field of complex numbers. The first question is to give an intrinsic…

We introduce the {\em $\mu$-topological stability}. This is a type of stability depending on the measure $\mu$ different from the set-valued approach \cite{lm}. We prove that the map $f$ is $m_p$-topologically stable if and only if $p$ is a…

We study geodesics along a noncompact Kerr-Newman instanton, where the asymptotic geometry is either de Sitter or anti-de Sitter. We use first integrals for the Hamilton-Jacobi equation to characterize trajectories both near and away from…

In a Riemannian manifold with a smooth positive function that weights the associated Hausdorff measures we study stable sets, i.e., second order minima of the weighted perimeter under variations preserving the weighted volume. By assuming…

Consider the H^{1/2}-critical Schroedinger equation with a cubic nonlinearity in R^3, i \partial_t \psi + \Delta \psi + |\psi|^2 \psi = 0. It admits an eight-dimensional manifold of periodic solutions called solitons e^{i(\Gamma + vx -…

We explore stability regions for solitons in the nonlinear Schrodinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign.…

We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in…

We study stability and local minimizing properties of $L^p$- norms of Riemannian curvature tensor denoted by $\mathcal{R}_p$ by variational methods. We compute the Hessian of $\mathcal{R}_p$ at compact rank 1 symmetric spaces and prove that…

In the frame of Gauss-Bonnet gravity and in the limit of $D\to 4$, based on the fact that spherically symmetric solution derived using any of regularization schemes will be the same form as the original theory…

We study a geometric flow on curves, immersed in $\mathbb{R}^3$, that have strictly positive torsion. The evolution equation is given by $$X_{t}=\frac{1}{\sqrt{\tau}} \textbf{B}$$ where $\tau$ is the torsion and $\textbf{B}$ is the unit…

For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.

We construct convex bodies that can be "captured by nets." More precisely, for each dimension $n \geq 2$, we construct a family of Riemannian $n$-spheres, each with a stable geodesic net, which is a stable 1-dimensional integral varifold.…

In the framework of Teleparallel Gravity, we derive a charged non-vacuum solution for a physically symmetric tetrad field with two unknown functions of radial coordinate. The field equations result in a closed-form adopting particular…

The analysis of contours of scalar fields plays an important role in visualization. For example the contour tree and contour statistics can be used as a means for interaction and filtering or as signatures. In the context of tensor field…

In this paper we study the strong stability of spacelike hypersurfaces with constant $r$-th mean curvature in Generalized Robertson-Walker spacetimes of constant sectional curvature. In particular, we treat the case in which the ambient…

In this article, we study the properties of the geodesic X-ray transform for asymptotically Euclidean or conic Riemannian metrics and show injectivity under non-trapping and no conjugate point assumptions. We also define a notion of lens…

We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem

We establish an approximate fixed point result for self-maps on compact convex subsets of Hausdorff topological vector spaces where continuity is not a necessary condition.

Utilizing the covariant formulation of Penrose's plane wave limit by Blau et~al., we construct for any semi-Riemannian metric $g$ a family of "plane wave limits." These limits are taken along any geodesic of $g$, yield simpler metrics of…

In this paper we consider the problem of finding $\epsilon$-approximate stationary points of convex functions that are $p$-times differentiable with $\nu$-H\"{o}lder continuous $p$th derivatives. We present tensor methods with and without…