Related papers: Injectivity and stability for a generic class of g…

In my talk I will discuss the following results which were obtained in joint work with Wilderich Tuschmann. 1. For any given numbers $m$, $C$ and $D$, the class of $m$-dimensional simply connected closed smooth manifolds with finite second…

We introduce a Bargmann transform on the space of hyperplanes by applying the Plancherel formula of the Radon transform to the definition of the Bargmann transform on the Euclidean space. Some basic facts on microlocal analysis are also…

We investigate the existence and regularity of locally invariant manifolds near an approximately invariant set that satisfies a geometric hyperbolicity condition with respect to an abstract ``generalized" dynamical system in Banach spaces.…

Let $\mathcal{G}(d,n)$ be the Grassmannian manifold of $n$-dimensional subspaces of $\mathbb{R}^{d}$, and let $\pi_{V} \colon \mathbb{R}^{d} \to V$ be the orthogonal projection. We prove that if $\mu$ is a compactly supported Radon measure…

In the theory of inner and outer balayage of positive Radon measures on a locally compact space $X$ to arbitrary $A\subset X$ with respect to suitable, quite general function kernels, developed in a series of the author's recent papers, we…

The inversion theorem for the k-plane Radon transform in R^n is often stated for Schwartz functions, and lately for smooth functions on R^n fulfilling that f(x)=O(|x|^{-N}) for some N>n. In this paper it will be shown, that it suffices to…

In this article, we consider a generalized Radon transform that comes up in ultrasound reflection tomography. In our model, the ultrasound emitter and receiver move at a constant distance apart along a circle. We analyze the microlocal…

In this paper, we study complete oriented $f$-minimal hypersurfaces properly immersed in a cylinder shrinking soliton $(\mathbb{S}^n\times \mathbb{R}, \bar{g}, f)$. We prove that such hypersurface with $L_f$-index one must be either…

A long standing conjecture, known to us as the Eisenbud Goto conjecture, states that an n-dimensional variety embedded with degree $d$ in the $N$- dimensional projective space is $(d-(N-n)+1)$-regular in the sense of Castelnuovo-Mumford. In…

We prove a persistence result for noncompact normally hyperbolic invariant manifolds in the setting of Riemannian manifolds of bounded geometry. Bounded geometry of the ambient manifold is a crucial assumption required to control the…

Let f, g be two homotopic smooth embeddings of a closed surface in a closed oriented 5-dimensional manifold. We show that if f admits a common algebraic dual 3-sphere, or if the fundamental group of the ambient space is trivial, then f and…

It is proved that any smooth manifold $\mathcal M$ of dimension $m$ admits a smooth polynomially convex embedding into $\mathbb C^n$ when $n\geq \lfloor 5m/4\rfloor$. Further, such embeddings are dense in the space of smooth maps from…

For the universal isomonodromic deformation of an irreducible logarithmic rank two connection over a smooth complex projective curve of genus at least two, consider the family of holomorphic vector bundles over curves underlying this…

We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds $(M,g)$ with $g \in C^{1,1}$. In addition to a proof, we produce a redefinition of simplicity that is…

This article introduces innovative classes of open sets in \(\mathbb{R}^{N}\), where \(N=2, 3\), characterized by a geometric property associated with the inward normal. The focus lies on proving compactness results for the Hausdorff…

A well-known result asserts that any isometric immersion with flat normal bundle of a Riemannian manifold with constant sectional curvature into a space form is (at least locally) holonomic. In this note, we show that this conclusion…

A number of practically important imaging problems involve inverting the generalized Radon transform (GRT) $\mathcal R$ of a function $f$ in $\mathbb R^3$. On the other hand, not much is known about the spatial resolution of the…

In [J. Bures, R. Lavicka, V. Soucek, Elements of quaternionic analysis and Radon transform, Textos de Matematica 42, Departamento de Matematica, Universidade de Coimbra, 2009], the authors describe a link between holomorphic functions…

Let X_0 be a compact connected Riemann surface of genus g with D_0\subset X_0 an ordered subset of cardinality n, and let E_G be a holomorphic principal G-bundle on X_0, where G is a complex reductive affine algebraic group, that admits a…

We prove that the unitary affine Radon transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation…