相关论文: On energy gap phenomena of the Whitney sphere and …

In \cite{Zh} \cite{LY} Zhang, Luo and Yin initiated the study of Lagrangian submanifolds satisfying ${\rm \nabla^*} T=0$ or ${\rm \nabla^*\nabla^*}T=0$ in $\mathbb{C}^n$ or $\mathbb{CP}^n$, where $T ={\rm \nabla^*}\tilde{h}$ and $\tilde{h}$…

For an immersed Lagrangian submanifold, let $\check{A}$ be the Lagrangian trace-free second fundamental form. In this note we consider the equation $\nabla^*T=0$ on Lagrangian surfaces immersed in $\mathbb{C}^2$, where…

In this paper we establish a gap phenomenon for immersed surfaces with arbitrary codimension, topology and boundaries that satisfy one of a family of systems of fourth-order anisotropic geometric partial differential equations. Examples…

Based on the seminal Simons' formula, Shen \cite{Shen} and Lin-Xia \cite{LX} obtained gap theorems for compact minimal submanifolds in the unit sphere in the late 1980's. Then due to the effect of Xu \cite{Xu}, Ni \cite{Ni}, Yun \cite{Yun}…

We propose a new mechanism for symmetry breaking in which, apart from particle degrees of freedom, topological degrees of freedom also emerge. In this method, a decomposition for the fields of the Yang-Mills-Higgs theory is introduced and…

The equations of Lagrangian gas dynamics fall into the larger class of overdetermined hyperbolic and thermodynamically compatible (HTC) systems of partial differential equations. They satisfy an entropy inequality (second principle of…

The notion of Lagrangian $H$-umbilical submanifolds was introduced by B. Y. Chen in 1997, and these submanifolds have appeared in several important problems in the study of Lagrangian submanifolds from the Riemannian geometric point of…

In this paper, based on the classical K. Yano's formula, we first establish an optimal integral inequality for compact Lagrangian submanifolds in the complex space forms, which involves the Ricci curvature in the direction $J\vec{H}$ and…

We use a Lagrangian regularity perspective to discuss resolvent estimates near zero energy on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. In addition to the Lagrangian perspective we introduce and…

We have discovered two unconstrained forms of free Lagrangian for continuous spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These Lagrangians, unlike that by Schuster and Toro, do not include delta functions and are…

We consider an O(N) version of a massive, interacting, chiral supersymmetry model solved exactly in the large N limit. We demonstrate that the system approaches a stable attractor at high energy densities, corresponding to a…

We use techniques based on the splitting tensor to explicitly integrate the Codazzi equation along the relative nullity distribution and express the second fundamental form in terms of the Jacobi tensor of the ambient space. This approach…

It was proved in [8,9] that every Lagrangian submanifold $M$ of a complex space form $\tilde M^{5}(4c)$ of constant holomorphic sectional curvature $4c$ satisfies the following optimal inequality: {align}\tag{A}\delta(2,2)\leq…

We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9-dimensional submanifold of the 12-dimensional…

We construct, for the first time, an off-shell supersymmetric continuous spin gauge theory in 4-dimensional Minkowski spacetime, in both constrained and unconstrained Lagrangian formulations. As an extension to the on-shell description [1],…

In this paper, we introduce a geometric flow for Lagrangian submanifolds in a K\"ahler manifold that stays in its initial Hamiltonian isotopy class and is a gradient flow for volume. The stationary solutions are the Hamiltonian stationary…

We study the topological entropy of the Lagrangian flow restricted to an energy level $E_{L}^{-1}(c) \subset TM$ for $ c >e_0(L)$. We prove that if the flow of the Tonelli Lagrangian $ L: M \to \mathbb{R}$, on a closed manifold of dimension…

The notion of Higgs-de Rham flows was introduced by Lan-Sheng-Zuo, as an analogue of Yang-Mills-Higgs flows in the complex nonabelian Hodge theory. In this short note we investigate a small part of this theory, and study those Higgs-de Rham…

The SM Lagrangian without physical scalars is rewritten as the LO of a Low-Energy Effective Theory invariant under a higher non linear symmetry S_{nat} \supset SU(2)_W \times U(1)_Y. Soft breaking of S_{nat} defines a hierarchy of non…

We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing $\mathcal{R}^5$ terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes.…