R. Rotman

activity

20022025

most citedContracting the boundary of a Riemannian 2-disc

11 citations · 17 across the 9 of their papers we have counts for

collaborators

14 papers

math.DG2025

Length of a closed geodesic in 3-manifolds of positive scalar curvature

Yevgeny Liokumovich, Davi Maximo, Regina Rotman

Let $M$ be a closed $3$ -dimensional Riemannian manifold with positive scalar curvature, $R_{g} \geq 6$ . We show that $M$ contains a non-trivial closed geodesic of length less than $2…

math.DG2024

Linear Bounds for the Lengths of Geodesics on Manifolds With Curvature Bounded Below

Isabel Beach, Haydeé Contreras Peruyero, Regina Rotman +1

Let $M$ be a simply connected Riemannian manifold in $M_{k, v}^{D} (n)$ , the space of closed Riemannian manifolds of dimension $n$ with sectional curvature bounded below by $…

math.DG2022

Geodesic nets on non-compact Riemannian manifolds

Gregory R. Chambers, Yevgeny Liokumovich, Alexander Nabutovsky +1

A geodesic flower is a finite collection of geodesic loops based at the same point $p$ that satisfy the following balancing condition: The sum of all unit tangent vectors to all ge…

math.DG2022

Positive Ricci Curvature and the Length of a shortest periodic geodesic

Regina Rotman

Let $M^{n}$ be a closed Riemannian manifold of dimension $n \geq 2$ , with Ricci curvature $R i c \geq n - 1$ . We will show that any sphere of dimension $m$ in the space of closed loops on…

math.DG2020

Sweepouts of closed Riemannian manifolds

Alexander Nabutovsky, Regina Rotman, Stéphane Sabourau

We show that for every closed Riemannian manifold there exists a continuous family of $1$ -cycles (defined as finite collections of disjoint closed curves) parametrized by a sphere…

math.DG2019★ 1 cited

The Length of the Shortest Closed Geodesic on a Surface of Finite Area

I. Beach, R. Rotman

In this paper we prove new upper bounds for the length of a shortest closed geodesic, denoted $l (M)$ , on a complete, non-compact Riemannian surface $M$ of finite area $A$ . We will…