42 citations · 90 across the 15 of their papers we have counts for
17 papers
Convexity inequalities for eigenvalues and log-concavity of eigenfunctions
Paul Bryan, Julie Clutterbuck, Cale Rankin
We give simple new proofs of two well-known results for the Schrödinger operator: first, the Brunn--Minkowski inequality for Dirichlet eigenvalues and, second, the log-concavity of…
Sharp distance comparison for curve shortening flow on the round sphere
Paul Bryan, Mat Langford, Jonathan J. Zhu
We prove that curve shortening flow on the round sphere displays sharp chord-arc improvement, precisely as in the planar setting (Andrews and Bryan, Comm. Anal. Geom., 2011). As in…
Constant rank theorems for curvature problems via a viscosity approach
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
An important set of theorems in geometric analysis consists of constant rank theorems for a wide variety of curvature problems. In this paper, for geometric curvature problems in c…
Parabolic approaches to curvature equations
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
We employ curvature flows without global terms to seek strictly convex, spacelike solutions of a broad class of elliptic prescribed curvature equations in the simply connected Riem…
Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings In Minkowski Space And The Cross Curvature Flow
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
This short note is a mostly expository article examining negatively curved three-manifolds. We look at some rigidity properties related to isometric embeddings into Minkowski space…
Li-Yau gradient estimates for curvature flows in positively curved manifolds
Paul Bryan, Heiko Kröner, Julian Scheuer
We prove differential Harnack inequalities for flows of strictly convex hypersurfaces by powers , , of the mean curvature in Einstein manifolds with a positive lower boun…