Connor Mooney

activity

20172022

most citedAn obstacle problem for conical deformations of thin elastic sheets

1 citations · 1 across the 7 of their papers we have counts for

collaborators

13 papers

math.AP2022

Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase

Arunima Bhattacharya, Connor Mooney, Ravi Shankar

In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and $C^{2}$ . Combined with the…

math.AP2022

Singular structures in solutions to the Monge-Ampère equation with point masses

Connor Mooney, Arghya Rakshit

We construct new examples of Monge-Ampère metrics with polyhedral singular structures, motivated by problems related to the optimal transport of point masses and to mirror symmetry…

math.AP2022

Homogeneous functions with nowhere vanishing Hessian determinant

Connor Mooney

We prove that functions that are homogeneous of degree $α \in (0, 1)$ on $R^{n}$ and have nowhere vanishing Hessian determinant cannot change sign.

math.AP2021

A proof by foliation that Lawson's cones are $A_{Φ}$ -minimizing

Connor Mooney, Yang Yang

We give a proof by foliation that the cones over $S^{k} \times S^{l}$ minimize parametric elliptic functionals for each $k, l \geq 1$ . We also analyze the behavior a…

math.AP2020

Strict $2$ -convexity of convex solutions to the quadratic Hessian equation

Connor Mooney

We prove that convex viscosity solutions to the quadratic Hessian inequality $σ_{2} (D^{2} u) \geq 1$ are strictly $2$ -convex. As a consequence we obtain short proofs of smoothness and i…

math.AP2020

Solutions to the Monge-Ampère equation with polyhedral and Y-shaped singularities

Connor Mooney

We construct convex functions on $R^{3}$ and $R^{4}$ that are smooth solutions to the Monge-Ampère equation $det D^{2} u = 1$ away from compact one-dimensional singular…

Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase

Singular structures in solutions to the Monge-Ampère equation with point masses

Homogeneous functions with nowhere vanishing Hessian determinant

A proof by foliation that Lawson's cones are AΦ​-minimizing

Strict 2-convexity of convex solutions to the quadratic Hessian equation

Solutions to the Monge-Ampère equation with polyhedral and Y-shaped singularities

A proof by foliation that Lawson's cones are $A_{Φ}$ -minimizing

Strict $2$ -convexity of convex solutions to the quadratic Hessian equation