Gunther Uhlmann

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20242026

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math.DG2026

The linearized minimal surfaces problem

Haim Grebnev, Plamen Stefanov, Gunther Uhlmann +1

We characterize the kernel of the linearization $R$ of the minimal surface problem about the Euclidean metric in a bounded smooth domain $Ω \subset R^{n}$ , $n \geq 2$ , with the b…

math.DG2024

Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors

Gunther Uhlmann, Jian Zhai

Consider a compact Riemannian manifold in dimension $n$ with strictly convex boundary. We show the local invertibility near a boundary point of the transverse ray transform of $2$ …

math.DG2024

Invertibility of local geodesic transverse and mixed ray transforms I: basic cases

Gunther Uhlmann, Jian Zhai

Consider a compact Riemannian manifold in dimension $n \geq 3$ with strictly convex boundary. We show that the transverse ray transform of $1$ tensors and the mixed ray transform of…