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Power Convexity of Solutions to a Special Lagrangian Equation in Dimension Two
In this paper, we prove power convexity result of solution to Dirichlet problem of special Lagrangian equation in dimension two. This provides new...
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On the second boundary value problem for special Lagrangian curvature potential equation
This is a sequel to (Huang and Ou in J Geom Anal 27:2601–2617, 2017) and (Chong et al. in On the second boundary value problem for Lagrangian mean...
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The Branched Deformations of the Special Lagrangian Submanifolds
In this paper, we investigate the branched deformations of immersed compact special Lagrangian submanifolds. If there exists a nondegenerate
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Special Lagrangian Cycles and Calabi-Yau Transitions
We construct special Lagrangian 3-spheres in non-Kähler compact threefolds equipped with the Fu–Li–Yau geometry. These non-Kähler geometries emerge...
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Classical Yang–Baxter Equation, Lagrangian Multiforms and Ultralocal Integrable Hierarchies
We cast the classical Yang–Baxter equation (CYBE) in a variational context for the first time, by relating it to the theory of Lagrangian multiforms,...
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Hessian estimates to special Lagrangian equation on general phases with constraints
We obtain a priori interior Hessian estimates to the special Lagrangian equation on general phases with constraints. Our results extend the classical...
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Liouville type theorems and Hessian estimates for special Lagrangian equations
In this paper, we get a Liouville type theorem for the special Lagrangian equation with a certain ’convexity’ condition, where Warren–Yuan first...
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On the existence of geodesics connecting Lagrangian graphs in Euclidean space
Existence theory for geodesics in the space of Lagrangian submanifolds plays an important role in a program for studying the existence and uniqueness...
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Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side
AbstractA model Helmholtz equation with a localized right-hand side is considered. When writing asymptotics of a solution satisfying the limit...
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On the second boundary value problem for Lagrangian mean curvature equation
Considering the second boundary value problem of the Lagrangian mean curvature equation, we obtain the existence and uniqueness of the smooth...
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Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen–Cahn Equation
The convective Allen–Cahn (CAC) equation has been widely used for simulating multiphase flows of incompressible fluids, which contains an extra...
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Counting special Lagrangian classes and semistable mukai vectors for K3 surfaces
Motivated by the study of the growth rate of the number of geodesics in flat surfaces with bounded lengths, we study generalizations of such problems...
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Asymptotic Expansion at Infinity of Solutions of Special Lagrangian Equations
We obtain a quantitative high-order expansion at infinity of solutions for a family of fully nonlinear elliptic equations on exterior domain, refine...
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Regularity of Critical Points of the Volume Functional for Lagrangian Submanifolds
We give a brief survey with emphasis on recent advances on regularity of solutions to the special Lagrangian equation and the Hamiltonian stationary...
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Hessian estimates for Lagrangian mean curvature equation
In this paper, we derive a priori interior Hessian estimates for the Lagrangian mean curvature equation if the Lagrangian phase is supercritical and...
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Mathematical Introduction to Special Relativity and the Relativistic Lagrangian Formulation
In this chapter we will discuss the mathematical principles underpinning the theory of Special Relativity from a geometrical and axiomatic point of...
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