https://neckpinch.com/authors/ravi-shankar/New arXiv papers by Ravi Shankar, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2510.22741/arxiv: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