4 papers
Extrinsic curvature flows and applications
Julian Scheuer
These notes arose from a mini lecture series the author gave at the Early Career Researchers Workshop on Geometric Analysis and PDEs, held in January 2020 at the Matrix institute o…
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…
Isoperimetric problems for spacelike domains in generalized Robertson-Walker spaces
Ben Lambert, Julian Scheuer
We use a locally constrained mean curvature flow to prove the isoperimetric inequality for spacelike domains in generalized Robertson-Walker spaces satisfying the null convergence…
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…