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math.AP2025
Doubling and the two-dimensional critical valued Lagrangian phase
Arunima Bhattacharya, Ravi Shankar, Jeremy Wall
In this paper, we establish interior Hessian and gradient estimates for the two-dimensional Lagrangian mean curvature equation when the phase changes signs, provided the gradient o…
math.AP2025
Singularities of the Lagrangian mean curvature flow at the critical Lagrangian phase
Arunima Bhattacharya, Ravi Shankar, Jeremy Wall +1
We establish interior estimates for singularities of the Lagrangian mean curvature flow when the Lagrangian phase is critical, i.e., , and extend our resul…
math.AP2025
Semi-convex viscosity solutions of the special Lagrangian equation
Connor Mooney, Ravi Shankar
We prove smoothness and interior derivative estimates for viscosity solutions to the special Lagrangian equation with almost negative phases and small enough semi-convexity. We sho…