Jared Marx-Kuo

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math.DG2026

Equivariant Allen--Cahn Solutions and the Existence of Cohomogeneity $2$ Minimal Surfaces

Rayssa Caju, Pedro Gaspar, Jared Marx-Kuo

We develop a regularity theory for equivariant Allen--Cahn solutions on closed Riemannian manifolds with a Lie group acting isometrically. When the cohomogeneity of the action is b…

math.DG2025

Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface

Pedro Gaspar, Jared Marx-Kuo

We construct infinitely many distinct hypersurfaces with prescribed mean curvature (PMC) for a large class of prescribing functions when $(M^{n + 1}, g)$ is a closed smooth manifold…

math.DG2025

Almgren's Three-Legged Starfish

Christos Mantoulidis, Jared Marx-Kuo

In this note we use classical tools from min-max and hyperbolic geometry to substantiate a folklore example in Almgren--Pitts min-max theory, the three-legged starfish metric on a…

math.DG2025

The p-widths of $R P^{2}$

Jared Marx-Kuo

We compute the p-widths, ${I ¨ _{p}}$ , for the real projective plane with the standard metric.

Equivariant Allen--Cahn Solutions and the Existence of Cohomogeneity 2 Minimal Surfaces

Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface

Almgren's Three-Legged Starfish

The p-widths of RP2

Equivariant Allen--Cahn Solutions and the Existence of Cohomogeneity $2$ Minimal Surfaces

The p-widths of $R P^{2}$