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

This article deals with stability issues related to geodesic X-ray transforms, where an interplay between the (attenuation type) weight in the transform and the underlying geometry strongly impact whether the problem is stable or unstable.…

We initiate a study of the inversion of the geodesic X-ray transform $I_m$ over symmetric $m$-tensor fields on asymptotically hyperbolic surfaces. This operator has a non-trivial kernel whenever $m\ge 1$. To propose a gauge representative…

This paper proves fixed domain asymptotic results for estimating a smooth invertible transformation $f:\Bbb{R}^2\to\Bbb{R}^2$ when observing the deformed random field $Z\circ f$ on a dense grid in a bounded, simply connected domain…

Consider a compact Riemannian manifold of dimension $\geq 3$ with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and…

The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear…

We propose a notion of stability for constant k-mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means…

Static spherically-symmetric matter distributions whose energy-momentum tensor is characterized by a non-negative trace are studied analytically within the framework of general relativity. We prove that such field configurations are…

Estimates for the norm of the second fundamental form, $|A|$, play a crucial role in studying the geometry of surfaces. In fact, when $|A|$ is bounded the surface cannot bend too sharply. In this paper we prove that for an embedded geodesic…

This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…

We introduce the boundary measure at scale r of a compact subset of the n-dimensional Euclidean space. We show how it can be computed for point clouds and suggest these measures can be used for feature detection. The main contribution of…

In this paper, we study stability and instability problem for type-II partitioning problem. First, we make a complete classification of stable type-II stationary hypersurfaces in a ball in a space form as totally geodesic $n$-balls. Second,…

We give an algorithm to compute the stable lengths of pseudo-Anosovs on the curve graph, answering a question of Bowditch. We also give a procedure to compute all invariant tight geodesic axes of pseudo-Anosovs. Along the way we show that…

We prove that the geodesic X-ray transform is injective on $L^2$ when the Riemannian metric is simple but the metric tensor is only finitely differentiable. The number of derivatives needed depends explicitly on dimension, and in dimension…

The determination of the stability of the long-lived consensus problem is a fundamental open problem in distributed systems. We concentrate on the memoryless binary case with geodesic paths. We offer a conjecture on the stability in this…

Closed sections of totally geodesic null hypersurfaces are marginally outer trapped surfaces (MOTS), for which a well-defined notion of stability exists. In this paper we obtain the explicit form for the stability operator for such MOTS and…

For a one-parameter family of simple metrics of constant curvature ($4\kappa$ for $\kappa\in (-1,1)$) on the unit disk $M$, we first make explicit the Pestov-Uhlmann range characterization of the geodesic X-ray transform, by constructing a…

This paper is concerned with the stability issue in determining absorption and diffusion coefficients in quantitative photoacoustic imaging. Assuming that the optical wave is generated by point sources in a region where the optical…

We consider nonstationary Stokes equations in nondivergence form with variable viscosity coefficients and generalized Navier slip boundary conditions with slip tensor $\mathcal{A}$ in a domain $\Omega$ in $\mathbb{R}^d$. First, under the…

The main concern of this paper is to mathematically investigate the formation of a plasma sheath near the surface of nonplanar walls. We study the existence and asymptotic stability of stationary solutions for the nonisentropic…

We study the geodesic X-ray transform $X$ on compact Riemannian surfaces with conjugate points. Regardless of the type of the conjugate points, we show that we cannot recover the singularities and therefore, this transform is always…