https://neckpinch.com/authors/mu-tao-wang/New arXiv papers by Mu-Tao Wang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.14444arxiv:2608.14444Fri, 14 Aug 2026 00:00:00 GMTTang-Kai Lee, Mu-Tao Wang — We introduce the almost isoclinic region in the oriented Lagrangian Grassmannian rm Lag⁺(n) of ℂⁿ, an intrinsic higher-dimensional analog of a natural convex region in rm Lag⁺(2) ≃ S¹× S². A Lagrangian submanifold is called almost isoclinic if its Gauss map takes values in this region, extending the graphical condition that the characteristic angles of the tangent plane remain uniformly close. We construct a canonical positive function Λ on this region and prove that log Λ is concave with respect to the invariant Grassmannian metric. This property yields subharmonicity and monotonicity formulas for minimal Lagrangians and Lagrangian mean curvature flow. As applications, we prove rigidity and Bernstein-type results, including that a complete connected almost isoclinic minimal Lagrangian with a positive lower bound for Λ must be a Lagrangian n-plane.Mean curvature flowLagrangian mean curvature flowStability & uniqueness https://arxiv.org/abs/2309.09432arxiv:2309.09432Mon, 18 Sep 2023 00:00:00 GMTChung-Jun Tsai, Mao-Pei Tsui, Mu-Tao Wang — Given an entire C² function u on ℝⁿ, we consider the graph of D u as a Lagrangian submanifold of ℝ²ⁿ, and deform it by the mean curvature flow in ℝ²ⁿ. This leads to the special Lagrangian evolution equation, a fully nonlinear Hessian type PDE. We prove long-time existence and convergence results under a 2-positivity assumption of (I+(D² u)²)⁻¹D² u. Such results were previously known only under the stronger assumption of positivity of D² u.Mean curvature flowLagrangian mean curvature flowLong-time existence & convergence https://arxiv.org/abs/2302.02512arxiv:2302.02512Mon, 06 Feb 2023 00:00:00 GMTChung-Jun Tsai, Mao-Pei Tsui, Mu-Tao Wang — We prove regularity, global existence, and convergence of Lagrangian mean curvature flows in the two-convex case. Such results were previously only known in the convex case, of which the current work represents a significant improvement. The proof relies on a newly discovered monotone quantity that controls two-convexity. Through a unitary transformation, same result for the mean curvature flow of area-decreasing Lagrangian submanifolds were established.Mean curvature flowLagrangian mean curvature flowLong-time existence & convergence https://arxiv.org/abs/2301.09222arxiv:2301.09222Sun, 22 Jan 2023 00:00:00 GMTChung-Jun Tsai, Mao-Pei Tsui, Mu-Tao Wang — A new monotone quantity in graphical mean curvature flows of higher codimensions is identified in this work. The submanifold deformed by the mean curvature flow is the graph of a map between Riemannian manifolds, and the quantity is monotone increasing under the area-decreasing condition of the map. The flow provides a natural homotopy of the corresponding map and leads to sharp criteria regarding the homotopic class of maps between complex projective spaces, and maps from spheres to complex projective spaces, among others.Mean curvature flow