46 citations · 460 across the 44 of their papers we have counts for
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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…
Minkowski inequalities and constrained inverse curvature flows in warped spaces
Julian Scheuer
This paper deals with locally constrained inverse curvature flows in a broad class of Riemannian warped spaces. For a certain class of such flows we prove long time existence and s…
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…
Concavity of solutions to degenerate elliptic equations on the sphere
Mat Langford, Julian Scheuer
We prove the concavity of classical solutions to a wide class of degenerate elliptic differential equations on strictly convex domains of the unit sphere. The proof employs a suita…