A Priori Estimates for Singularities of the Lagrangian Mean Curvature Flow with Supercritical Phase

Arunima Bhattacharya; Jeremy Wall

A Priori Estimates for Singularities of the Lagrangian Mean Curvature Flow with Supercritical Phase

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arxiv 2407.12756 v2 pith:PDZYQP6F submitted 2024-07-17 math.AP math.DG

Arunima Bhattacharya , Jeremy Wall This is my paper · ORCID

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keywords lagrangiancurvaturemeanphasesupercriticalestimatesflowpriori

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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.

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Removing singularities for fully nonlinear PDEs
math.AP 2024-11 conditional novelty 6.0 of 10

Half-line singularities of viscosity solutions are removable for fully nonlinear elliptic PDEs with a Jacobi inequality, proven by a doubling argument; the single-side version is new.

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