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Maslov Index on Symplectic Manifolds. With Supplement by A. T. Fomenko “Constructing the Generalized Maslov Class for the Total Space \(W=\mathbb{T}^*(M)\) of the Cotangent Bundle”
AbstractThe geometric properties of the Maslov index on symplectic manifolds are discussed. The Maslov index is constructed as a homological...
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Displaceability of Certain Constant Sectional Curvature Lagrangian Submanifolds
We present an alternative proof of a nonexistence result for displaceable constant sectional curvature Lagrangian submanifolds under certain...
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A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds
This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth...
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Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge
We consider an autonomous, indefinite Lagrangian L admitting an infinitesimal symmetry K whose associated Noether charge is linear in each tangent...
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The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model
In general, the system of 2nd-order partial differential equations made of the Euler–Lagrange equations of classical field theories are not...
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Ungraded Matrix Factorizations as Mirrors of Non-orientable Lagrangians
We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds. An ungraded matrix factorization of a...
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Multisymplectic Lagrangian Models in Gravitation
We apply the multisymplectic formulation of classical field theories [12, 13, 15] to describe the Einstein–Hilbert and the Einstein–Palatini (or...
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A Minimal Maslov Number Condition for Displaceability in Certain Weakly Exact Symplectic Manifolds
We present a proof of a result which gives an upper bound for the minimal Maslov number of a displaceable n-dimensional Lagrangian submanifold in a...
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Constructions of Lagrangian Cobordisms
Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not well-understood relation on...
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Time-dependent contact mechanics
Contact geometry allows us to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to...
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Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves...
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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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On Lagrangian and Legendrian Singularities
We describe the topology of stable simple multisingularities of Lagrangian and Legendrian maps. In particular, the tables of adjacency indices of...
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An Approximate Augmented Lagrangian Method for Nonnegative Low-Rank Matrix Approximation
Nonnegative low-rank (NLR) matrix approximation, which is different from the classical nonnegative matrix factorization, has been recently proposed...
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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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Recent Developments on Chen–Ricci Inequalities in Differential Geometry
One of the most fundamental interests in submanifold theory is to establish simple relationships between the main extrinsic invariants and the main...
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On the compactness of Hamiltonian stationary Lagrangian surfaces in Kähler surfaces
We prove a bubble tree convergence theorem for a sequence of closed Hamiltonian stationary Lagrangian surfaces with bounded areas and Willmore...
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Infinitesimally tight Lagrangian orbits
We describe isotropic orbits for the restricted action of a subgroup of a Lie group acting on a symplectic manifold by Hamiltonian symplectomorphisms...