https://neckpinch.com/authors/jeremy-wall/New arXiv papers by Jeremy Wall, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2510.22741arxiv:2510.22741Sun, 26 Oct 2025 00:00:00 GMTArunima Bhattacharya, Ravi Shankar, Jeremy Wall, Diego Yepez — We establish interior estimates for singularities of the Lagrangian mean curvature flow when the Lagrangian phase is critical, i.e., |Θ|≥ (n-2)tfracπ2, and extend our results to the broader class of Lagrangian mean curvature type equations. Our gradient estimates require certain structural conditions, and we construct C^α singular viscosity solutions to show that criticality of the phase is necessary, and that these conditions cannot be removed in dimension one. We also introduce a new method for proving C^(2,α) estimates by exponentiating the arctangent operator into a concave one when |Θ|≥ (n-2)tfracπ2 and n>2.Mean curvature flowLagrangian mean curvature flowSingularitiesWeak & singular flows https://arxiv.org/abs/2407.12756arxiv:2407.12756Wed, 17 Jul 2024 00:00:00 GMTArunima Bhattacharya, Jeremy Wall — In this paper, we prove interior a priori estimates for singularities of the Lagrangian mean curvature flow assuming the Lagrangian phase is supercritical. We prove a Jacobi inequality that holds good when the Lagrangian phase is critical and supercritical. We further extend our results to a broader class of Lagrangian mean curvature type equations.Mean curvature flowLagrangian mean curvature flowSingularities https://arxiv.org/abs/2403.07235arxiv:2403.07235Tue, 12 Mar 2024 00:00:00 GMTArunima Bhattacharya, Jeremy Wall — In this paper, we prove interior Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian mean curvature flow under the assumption that the Lagrangian phase is hypercritical. We further extend our results to a broader class of Lagrangian mean curvature type equations.Mean curvature flowLagrangian mean curvature flowRicci solitonsSelf-shrinkers & translators