Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0904.3804

Calderon inverse Problem for the Schrodinger Operator on Riemann Surfaces

Colin Guillarmou·Leo Tzou
View original source ↗Read source document ↗Export metadata ↓

Abstract

On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that the Cauchy data space (or Dirichlet-to-Neumann map $\mc{N}$) of the Schrödinger operator $Δ+V$ with $V\in C^2(M_0)$ determines uniquely the potential $V$. We also discuss briefly the corresponding consequences for potential scattering at 0 frequency on Riemann surfaces with asymptotically Euclidean or asymptotically hyperbolic ends.

Explore related subjects

math.DGmath.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Colin Guillarmou, Leo Tzou. 2009-04-24. Calderon inverse Problem for the Schrodinger Operator on Riemann Surfaces. https://arxiv.org/abs/0904.3804

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Futaki invariant on Hopf manifolds

The Futaki invariant is a fundamental tool in Kähler geometry representing an obstruction to the existence of Kähler-Einstein metrics. Recently, it was generalized to compact complex manifolds. In this paper, we prove that it vanishes on Hopf manifolds.

math.DG↗
arXiv2026

Remarks on potential functions of noncompact quasi-Einstein manifolds

In this article, we study the set of potential functions on noncompact quasi-Einstein manifolds. We show that the space of all positive potential functions on a three-dimensional noncompact quasi-Einstein manifold has dimension at most two, and that equality holds if and only if the manifold is isometric to a product $B\times\mathbb{R}$, where $B$ is a $λ$-Einstein surface or one of the examples obtained by L. Berard Bergery and described in Besse's book. Moreover, we prove that any asymptotically flat $n$-dimensional quasi-Einstein manifold with $λ=0$ is necessarily Ricci-flat.

math.DG↗
arXiv2026

Adjusted connections on non-abelian bundle gerbes

Higher gauge theory for non-abelian structure 2-groups faces significant challenges when extending beyond the fake-flat sector, which suffers from limited applicability in physical models. A promising resolution involves equipping 2-groups with additional structure, known as adjustments. We present a comprehensive theory of adjusted connections on non-abelian bundle gerbes, classified by Saemann's adjusted version of non-abelian differential cohomology. This theory enables, in particular, a new coordinate-independent formulation of Tellez-Dominguez' lifting theorem, establishing a correspondence between adjusted connections on non-abelian bundle gerbes and connections on abelian bundle 2-gerbes.

math.DG↗