arXiv subjects
Publications and source records attributed to Evangelia Samiou.
In symmetric spaces of rank one we obtain a right inverse of the Cartan differential on exact differential forms as an integral operator. As a corollary we extend Gauss linking integral beyond space forms.
We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior differential on closed forms with image in the kernel of the codifferential. Any Biot-Savart operator gives rise to a Gauss linking integral.
This article is concerned with support theorems of the X-ray transform on non-compact manifolds with conjugate points. In particular, we prove that all simply connected 2-step nilpotent Lie groups have a support theorem. Important ingredients of the proof are the concept of plane covers and a support theorem for simple manifolds by Krishnan.We also provide examples of non-homogeneous 3-dimensional simply connected manifolds with conjugate points which have support theorems.
We prove injectivity and a support theorem for the X-ray transform on $2$-step nilpotent Lie groups with many totally geodesic $2$-dimensional flats. The result follows from a general reduction principle for manifolds with uniformly escaping geodesics.
We study integral geometric properties of non-compact harmonic spaces.
We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems.
We classify all simply connected Riemannian manifolds whose isotropy groups act with cohomogeneity less than or equal to two.
We determine the moduli space of metric 2-step nilpotent Lie algebras of dimension up to 6. This space is homeomorphic to a cone over a 4-dimensional contractible simplicial complex.
We show that the Cheeger isoperimetric constant of a solvable simply connected Lie group $G$ with Lie algebra $\G$ is $h(G)=\max_{H\in\G,||H||=1} \tr(\ad (H))$.