James Marshall Reber

collaborators

5 papers

math.DS2026

On the creation of conjugate points for thermostats

Javier EchevarrÃa Cuesta, James Marshall Reber

Let $(M, g)$ be a closed oriented Riemannian surface, and let $S M$ be its unit tangent bundle. We show that the interior in the $C^{2}$ topology of the set of smooth functi…

math.DS2026

Thermostats without conjugate points

Javier EchevarrÃa Cuesta, James Marshall Reber

We generalize Hopf's theorem to thermostats: the total thermostat curvature of a thermostat without conjugate points is non-positive and vanishes only if the thermostat curvature i…

math.DG2024

A counterexample to marked length spectrum semi-rigidity

Andrey Gogolev, James Marshall Reber

Given a closed orientable negatively curved Riemannian surface $(M, g)$ , we show how to construct a perturbation $(M, g^{'})$ such that each closed geodesic becomes longer, and ye…

math.DG2024

Magnetic flatness and E. Hopf's theorem for magnetic systems

Valerio Assenza, James Marshall Reber, Ivo Terek

Using the notion of magnetic curvature recently introduced by the first author, we extend E. Hopf's theorem to the setting of magnetic systems. Namely, we prove that if the magneti…

math.DG2024

Deformative Magnetic Marked Length Spectrum Rigidity

James Marshall Reber

Let $M$ be a closed surface and let ${g_{s} ∣ s \in (- I^µ, I^µ)}$ be a smooth one-parameter family of Riemannian metrics on $M$ . Also let $\{Îº_s : M \rightarrow \mathbb{R} \ | \…