Related papers: The Morse index theorem for regular Lagrangian sys…

In this paper, we prove the boundary partial regularity for a class of coupled Dirac-harmonic maps satisfying a certain energy monotonicity inequality near the boundary.

On any surface we give an example of a metric that contains simple closed geodesics with arbitrary high Morse index. Similarly, on any 3-manifold we give an example of a metric that contains embedded minimal tori with arbitrary high Morse…

We consider a {\em Hamiltonian setup} $\sextuple$, where $(\mathcal M,\omega)$ is a symplectic manifold, $\mathfrak L$ is a distribution of Lagrangian subspaces in $\mathcal M$, $\mathcal P$ a Lagrangian submanifold of $ \mathcal M$, $H$ is…

We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…

We derive Moore-type upper bounds for regular simplicial complexes and present logarithmic lower bounds on their diameter based on minimum degree.

The paper is devoted to an analogue of Atiyah-Bott-Singer index theorem for families of self-adjoint elliptic (i.e. satisfying the Shapiro-Lopatinskii condition) local boundary problems of order 1. The proofs are based on classical…

We systematically derive the Lax pair formulation for both discrete and continuum integrable classical theories with consistent boundary conditions.

Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…

We prove Shokurov's index conjecture for quotient singularities.

We develop a Hamilton-Jacobi theory for singular lagrangian systems using the Gotay-Nester-Hinds constraint algorithm. The procedure works even if the system has secondary constraints.

One approach to studying the dynamics of a singular Lagrangian system is to attempt to regularize it, that is, to find an equivalent and regular system. In the case of time-independent singular Lagrangians, an approach due to \textit{A.…

We explain how to generalize Lazzarini's structural Theorem from [Laz11] to the case of curves with boundary on a given Lagrangian immersion. As a consequence of this result, we show that we can compute Floer homology with time-independent…

We propose to interpret Levinson's theorem as an index theorem. This exhibits its topological nature. It furthermore leads to a more coherent explanation of the corrections due to resonances at thresholds.

In this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains. The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy…

In this paper, we give the definition of Maslov-type index of the discrete Hamiltonian system, and obtain the relation of Morse index and Maslov-type index of the discrete Hamiltonian system which is a generalization of case $\omega=1$ in…

We find various lower and upper bounds for the index of Wente tori that contain a continuous family of planar principal curves. We then prove a result that gives an algorithm for computing the index sharply.

In this paper, we compute the Morse index of rotationally symmetric minimal Y-singular surfaces under assumption that the Y-singularities form a single circle. This computation is carried out by utilizing information from two simpler…

This is the second paper in our sequence. Here, we apply our abstract Morse index formulation developed in the previous paper to study several optimization set-ups with constraints, including type I or/and type II considerations. A common…

In this note, we first introduce a boundary problem for Lagrangian submanifolds, analogous to the problem for free boundary hypersurfaces and capillary hypersurfaces. Then we present several interesting examples of Lagrangian submanifolds…

In this paper, we establish the existence and uniqueness theorem of the exterior Dirichlet problem for special Lagrangian equations with prescribed asymptotic behavior at infinity.