Internal Lagrangians derived from variational principles.
problem Reproducing the principle of stationary action in variational geometry.
method Introducing stationary points of internal Lagrangians, establishing connections with symmetries and conservation laws, and investigating relations between non-degenerate and internal Lagrangians.
result Noether's theorem reformulated in terms of internal Lagrangians.
Introduces internal Lagrangians for differential equations and connects them to presymplectic structures.
problem Understanding the geometry of differential equations and their solutions.
method Develops a spectral sequence related to internal Lagrangians and investigates connections to presymplectic structures.
result Interprets a term in Vinogradov's spectral sequence for gauge theories.
New approach to Lagrangian systems using intrinsic geometry.
problem Developing a new framework for Lagrangian systems.
method Direct reformulation of Hamiltonian formalism, introduction of spatial equation and spatial-gauge symmetry.
result Covariant and non-covariant canonical variational principles demonstrated for Maxwell equations.
Proves finiteness and holonomicity of skein modules for 3-manifolds.
problem Finiteness and holonomicity of skein modules for 3-manifolds.
method Defining skein transfer bimodules and using q-analogues of D-module theory.
result Internal skein modules are holonomic modules over the internal skein algebra of the boundary.
This article is a continuation of earlier work [R.L. Huang and Y.H. Ye, On the second boundary value problem for a class of fully nonlinear flows I, to appear in International Mathematics Research Notices], where the long time existence and convergence were given on some general parabolic type special Lagrangian equati…
This thesis is devoted to various questions connected with duality. It is composed of two parts. The first part discusses some aspects of timelike T-duality. We explore the possibility of compactification of supergravity theories with various signatures (low energy limit of M-theories which are dual under timelike T-…
IAs is well known, when D6 branes wrap a special lagrangian cycle on a non compact CY 3-fold in such a way that the internal string frame metric is Kahler there exists a dual description, which is given in terms of a purely geometrical eleven dimensional background with an internal metric of G2 holonomy. It is also …
Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle vanishes. However, only two field models meet this property in fact. In gauge theory of…
Paper offers a dual formulation for consumption problem with multiplicative habit.
problem Optimal consumption with multiplicative habit formation.
method Dual formulation using Fenchel's Duality Theorem.
result Strong duality result linking primal and dual controls.
Model predicts internal fraud in retail banking is cyclical and influenced by corruption.
problem Predicting and mitigating internal fraud losses in retail banking.
method Developed a dynamic model considering internal factors and macroeconomic indicators.
result Internal fraud losses are pro-cyclical and positively affected by corruption perceptions.
Examines international taxation's impact on Georgian businesses.
problem Impact of international taxation on Georgian business entities.
method Analyzes types, features, and approaches of international taxation.
result Provides recommendations to correct current taxation issues.
Optimized execution model using interbank and internal liquidity.
problem Minimizing market impact in trading.
method Integrates interbank limit and market orders with internal market-making liquidity.
result Reduces market impact and improves execution efficiency.
Constructing translating solitons from Lagrangian Grim Reapers.
problem Creating Lagrangian translating solitons from intersections of Grim Reapers.
method Desingularizing intersections with special Lagrangian Lawlor necks.
result Constructing Lagrangian translating solitons with multiple ends and loops.
In this paper, we study the Lagrangian F-stability of closed Lagrangian self-shrinkers immersed in complex Euclidean space. We show that any closed Lagrangian self-shrinker with first Betti number greater than one is Lagrangian F-unstable. In particular, any two-dimensional embedded closed Lagrangian self-shrinker is L…
This study assesses how economic shocks affect the efficiency and robustness of international pesticide trade networks.
problem Economic shocks impact the efficiency and robustness of international pesticide trade networks.
method Simulations were used to quantify efficiency and robustness under different economic shocks. Three strategies were tested: descending, random, and ascending node removal.
result The international pesticide trade networks became more efficient and robust except for clustering coefficient. Import-oriented economies were more vulnerable to shocks.
We exhibit infinitely many, explicit special Lagrangian isolated singularities that admit no asymptotically conical special Lagrangian smoothings. The existence/ nonexistence of such smoothings is an important component of the current efforts to understand which singular special Lagrangians arise as limits of smooth sp…
We introduce a notion of vanishing Maslov index for lagrangian varifolds and lagrangian integral cycles in a Calabi-Yau manifold. We construct mass-decreasing flows of lagrangian varifolds and lagrangian cycles which satisfy this condition. The flow of cycles converges, at infinite time, to a sum of special lagrangian …
Study on singularities of Lagrangian immersions with applications in Floer theory.
problem Understanding singularities of Lagrangian immersions.
method Applying Hamiltonian isotopy in the Weinstein tubular neighbourhood to express singular points as fold points with cusp points.
result Local expression of singular points of Lagrangian immersions as fold points with cusp points.
There are few papers about the international trade of flowers, so it is believed that this paper, with this topic, could be an important contribution to the international scientific community. It is intended to analyze if the international trade flowers tendencies and policies are adapted to the actual world global con…
Spain uses DEA to select international markets for exports.
problem Choosing the best international markets for Spanish exports.
method Output-oriented DEA model considering multiple validated inputs and outputs.
result Identifies efficient regions generating higher benefits with lower costs.
Improved speech recognition model with better performance.
problem Speech recognition accuracy on Librispeech.
method Integrates an external language model with an internal LM correction.
result Over 14% relative improvement in performance.
New method fills cluster seeds with exact Lagrangian structures.
problem Surjectivity of map from Lagrangian fillings to cluster seeds.
method Construction of quiver with potential and Lagrangian disk surgeries.
result Trivial deformation space of quiver allows manipulation of fillings.
Quantifies closeness of special Lagrangians under Floer conditions.
problem Estimating closeness of special Lagrangians.
method Floer theoretic conditions leading to quantitative estimates.
result Strong-weak uniqueness theorem for special Lagrangians.
In this paper, we prove that any Lagrangian translating soliton is Lagrangian L-stable.
Proves conditions for generating families on Lagrangian cobordisms.
problem Existence of generating families on Lagrangian cobordisms.
method Analyzes exact Lagrangian cobordisms and Legendrian submanifolds using generating families.
result Conditions for extending generating families linear at infinity.
Ancient solutions and translators identified for Lagrangian flow.
problem Characterizing ancient solutions and translators of Lagrangian mean curvature flow.
method Analyzing almost calibrated, exact, ancient solutions with specific geometric properties.
result All ancient solutions with entropy less than 3 are special Lagrangian, planes, or translators in \(\mathbb{C}^2\).
Geodesics in positive Lagrangian spaces map to special Lagrangian cylinders.
problem Understanding geodesics in spaces of positive Lagrangian submanifolds.
method Cylindrical transform of geodesics, solving elliptic PDEs.
result Geodesics in positive Lagrangian spaces correspond to one-parameter families of special Lagrangian cylinders.
New findings show that some knotted surfaces remain distinct even after many stabilizations.
problem Understanding the behavior of knotted surfaces after internal stabilizations.
method Analyzing the properties of smoothly knotted surfaces and their behavior under internal stabilizations.
result There is no upper bound on the number of internal stabilizations required for some knotted surfaces to remain distinct.
H-minimal Lagrangian submanifolds in general Kähler manifolds generalize special Lagrangian submanifolds in Calabi-Yau manifolds. In this paper we will use the deformation theory of H-minimal Lagrangian submanifolds in Kähler manifolds to construct minimal Lagrangian torus in certain Kähler-Einstein manifolds with nega…
Proves a conjecture about Lagrangian intersections using new theory.
problem Homological Arnol'd conjecture on Lagrangian intersections.
method New Lagrangian Ljusternik-Schnirelman theory and fundamental quantum factorizations.
result Uniform lower bounds on Lagrangian intersection numbers.
We study singularities of Lagrangian mean curvature flow in $\C^n$ when the initial condition is a zero-Maslov class Lagrangian. We start by showing that, in this setting, singularities are unavoidable. More precisely, we construct Lagrangians with arbitrarily small Lagrangian angle and Lagrangians which are Hamiltonia…
Classifies actions on complex space forms with Lagrangian orbits.
problem Classifying actions on complex space forms with Lagrangian orbits.
method Classifies holomorphic isometric actions on complex space forms.
result Only examples are Lagrangian affine subspace foliations of complex Euclidean spaces and Lagrangian horocycle foliations of complex hyperbolic spaces.
Study exact Lagrangian cobordisms in cotangent bundles, proving bounds on sheaf interleaving distance and shadow distance.
problem Understanding Lagrangian cobordisms and their properties in cotangent bundles.
method Use microlocal theory of sheaves, sheaf quantization, and cone decompositions.
result Interleaving distance of sheaves is bounded by the shadow distance of the cobordism.
Paper proves estimates for Lagrangian flow singularities.
problem Understanding Lagrangian flow singularities.
method Interior a priori estimates and Jacobi inequality.
result Proves estimates for supercritical Lagrangian phase.
In this paper we first give a Bonnet theorem for conformal Lagrangian surfaces in complex space forms, then we show that any compact Lagrangian surface in the complex space form admits at most one other global isometric Lagrangian surface with the same mean curvature form, unless the Maslov form is conformal. These two…
In this paper we use Floer theory to study topological restrictions on Lagrangian embeddings in closed symplectic manifolds. One of the phenomena arising from our results is ``homological rigidity'' of Lagrangian submanifolds. Namely, in certain symplectic manifolds, conditions on low dimensional topological invariants…
We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperkahler manifold. We establish a characterization, a Chern number inequality, topological and geometrical properties of Lagrangian submanifolds. We discuss a category of Lagrangian subvarieties and its relationship with the…
In this paper we show how to lift Lagrangian immersions in CPn−1 to produce Lagrangian cones in Cn, and use this process to produce several families of examples of Lagrangian cones and special Lagrangian cones. Moreover we show how to produce Lagrangian cones, isotopic to the Harvey-Lawson a…
Proves nearby Lagrangian cocores are homotopically rigid in certain dimensions.
problem Homotopy rigidity of nearby Lagrangian cocores in Weinstein sectors.
method Spectral wrapped Donaldson-Fukaya category with orthogonal group coefficients.
result Inclusion followed by retract and quotient is null-homotopic.
Derives Hessian estimates for Lagrangian mean curvature equation.
problem Lagrangian mean curvature equation with supercritical phase and bounded second derivatives.
method Derives a priori interior Hessian estimates.
result Hessian estimates for Lagrangian mean curvature equation.
The paper classifies certain types of Lagrangian translators and self-expanders in complex 2-space.
problem Classifying Lagrangian translators and self-expanders in complex 2-space.
method Using a new Omori-Yau type maximum principle proved by Chen and Qiu.
result Several classification results of 2-dimensional complete Lagrangian translators and self-expanders.
The abstract discusses special Lagrangians and their flow, proving conjectures and observing related phenomena.
problem Existence and long-time existence of special Lagrangian representatives and Lagrangian mean curvature flow.
method Gibbons-Hawking ansatz, circle-invariant hyperkaehler 4-manifolds, Calabi-Yau 2-folds, Thomas conjecture, Thomas-Yau conjecture.
result Proves versions of the Thomas conjecture and Thomas-Yau conjecture.
The paper studies Lagrangian surfaces in a specific Riemannian product space.
problem Characterizing and classifying Lagrangian surfaces in a particular geometric space.
method Analyzes various types of Lagrangian surfaces and their properties.
result Classification of different types of Lagrangian surfaces.
Generalizes Thomas-Yau theorem for special and minimal Lagrangians.
problem Proving uniqueness of special Lagrangians and minimal Lagrangians.
method Hamiltonian perturbations using Imagi, Joyce, and Oliveira dos Santos method.
result Generalized uniqueness theorem for special and minimal Lagrangians.
4-dim intrinsic (material) Riemannian metric G of the material 4-D space-time continuum P is utilized as the characteristic of the aging processes developing in the material. Manifested through variation of basic material characteristics such as density, moduli of elasticity, yield stress, strength, and toughness.,…
Paper solves flat bi-Lagrangian structure problems in ray space.
problem Existence of flat bi-Lagrangian structures in ray space.
method Established geometric conditions for flat canonical connections.
result Complete solutions to two problems regarding flat bi-Lagrangian structures.
This paper develops a non-Bayesian methodology to analyze the time-varying structure of international linkages and market efficiency in G7 countries. We consider a non-Bayesian time-varying vector autoregressive (TV-VAR) model, and apply it to estimate the joint degree of market efficiency in the sense of Fama (1970, 1…
New Lagrangian and special Lagrangian examples found in complex space.
problem Constructing exact Lagrangian and special Lagrangian submanifolds with symmetries.
method Using an Ansatz generalizing Castro-Lerma's construction, with admissible compact and non-compact subgroups.
result Explicit examples of Lagrangian translators and special Lagrangians with various symmetries.