6 citations · 8 across the 13 of their papers we have counts for
15 papers
Constructing entire minimal graphs by evolving planes
Chung-Jun Tsai, Mao-Pei Tsui, Jingbo Wan +1
We introduce an evolving-plane ansatz for the explicit construction of entire minimal graphs of dimension () and codimension (), for any odd integer .…
An ansatz for constructing explicit solutions of Hessian equations
Chung-Jun Tsai, Mao-Pei Tsui, Mu-Tao Wang
We introduce a (variation of quadrics) ansatz for constructing explicit, real-valued solutions to broad classes of complex Hessian equations on domains in and re…
Entire solutions of two-convex Lagrangian mean curvature flows
Chung-Jun Tsai, Mao-Pei Tsui, Mu-Tao Wang
Given an entire function on , we consider the graph of as a Lagrangian submanifold of , and deform it by the mean curvature flow in $…
Mean Curvature Flows of Two-Convex Lagrangians
Chung-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 whi…
A New Monotone Quantity in Mean Curvature Flow Implying Sharp Homotopic Criteria
Chung-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 m…
An Isoperimetric-Type Inequality for Spacelike Submanifold in the Minkowski Space
Chung-Jun Tsai, Kai-Hsiang Wang
We prove an isoperimetric-type inequality for maximal, spacelike submanifold in the Minkowski space. The argument is based on the recent work of Brendle.
Global uniqueness of the minimal sphere in the Atiyah-Hitchin manifold
Chung-Jun Tsai, Mu-Tao Wang
In this note, we study submanifold geometry of the Atiyah-Hitchin manifold, the double cover of the -monopole moduli space. When the manifold is naturally identified as the tota…
A strong stability condition on minimal submanifolds and its implications
Chung-Jun Tsai, Mu-Tao Wang
We identify a strong stability condition on minimal submanifolds that implies uniqueness and dynamical stability properties. In particular, we prove a uniqueness theorem and a C^1…
Mean curvature flows in manifolds of special holonomy
Chung-Jun Tsai, Mu-Tao Wang
We study the uniqueness of minimal submanifolds and the stability of the mean curvature flow in several well-known model spaces of manifolds of special holonomy. These include the…
Cohomology and Hodge Theory on Symplectic Manifolds: III
Chung-Jun Tsai, Li-Sheng Tseng, Shing-Tung Yau
We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered…
Dirac spectral flow on contact three manifolds II: Thurston--Winkelnkemper contact forms
Chung-Jun Tsai
Given an open book decomposition of a three manifold , Thurston and Winkelnkemper [TW] construct a specific contact form on . Given a spin-c Dirac operator on…
Dirac spectral flow on contact three manifolds I: eigensection estimates and spectral asymmetry
Chung-Jun Tsai
Let be a compact, oriented 3-manifold with a contact form and a metric . Suppose that is a principal bundle with structure group $U(2) = SU(2)\times_{\pm1}S^…
Asymptotic spectral flow for Dirac operators of disjoint Dehn twists
Chung-Jun Tsai
Let Y be a compact, oriented 3-manifold with a contact form a. For any Dirac operator D, we study the asymptotic behavior of the spectral flow between D and D+cl(-ira) as r very la…
Cohomology and Hodge Theory on Symplectic Manifolds: II
Li-Sheng Tseng, Shing-Tung Yau
We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in c…
Cohomology and Hodge Theory on Symplectic Manifolds: I
Li-Sheng Tseng, Shing-Tung Yau
We introduce new finite-dimensional cohomologies on symplectic manifolds. Each exhibits Lefschetz decomposition and contains a unique harmonic representative within each class. Ass…