The study proves conditions for Hermitian metrics on compact almost complex manifolds.
problem Conditions for Hermitian metrics on compact almost complex manifolds.
method Analyzes compact almost complex manifolds with Hermitian metrics and integral conditions involving ∂-harmonic (0,1)-forms. result The integral condition is automatically satisfied for strongly Gauduchon metrics, and equivalent to being strongly Gauduchon for integrable almost complex structures.
Study constant mean curvature surfaces with integrable boundary conditions.
problem Understanding surfaces with constant mean curvature under specific boundary conditions.
method Used generalized Weierstrass representation to determine potentials.
result Determined potentials for surfaces satisfying integrable boundary conditions.
The paper generalizes Alexandrov theorems for null hypersurfaces with integral curvature conditions.
problem Determining when a submanifold lies on a shear-free null hypersurface under integral curvature conditions.
method Using Minkowski formulas with arbitrary weight to derive rigidity results for submanifolds with weaker integral curvature conditions.
result A necessary and sufficient condition for a submanifold to lie in a shear-free null hypersurface is given by a mean curvature integral inequality.
We give a necessary and sufficient condition on the 1-jet of a field of nilpotent endomorphisms to be integrable. Together with the well known corresponding condition for an almost complex structure, the nullity of its Nijenhuis tensor, this gives an integrability condition for any field of endomorphisms.
Develops a new integration theory for financial markets.
problem No classical measure theory applies to financial markets.
method Introduces conditional non-lattice integrals for non-lattice vector spaces.
result Validates the new integration theory through hedging and pricing.
Defines strongest integrability condition for skew-symmetric endomorphisms.
problem Integrability conditions for skew-symmetric endomorphisms.
method Characterization of the shifted Courant-Nijenhuis torsion.
result Vanishing of the shifted Courant-Nijenhuis torsion as the strongest integrability condition.
Study of Killing spinor-valued forms and their integrability conditions.
problem Understanding Killing spinor-valued forms and their properties.
method Detailed treatment of prolongation and integrability conditions, relating to curvature of the manifold.
result New solutions found that are not from tensor products of Killing spinors and Killing-Yano forms.
Coercivity condition ensures learning of interacting particle systems.
problem Ensuring identifiability of interaction functions in learning systems of interacting particles.
method Equivalence of coercivity condition to strictly positive definiteness of an integral kernel.
result For ergodic systems, the integral kernel is strictly positive definite, satisfying the coercivity condition.
We use an isomorphism between the space of valence two Killing tensors on an n-dimensional constant sectional curvature manifold and the irreducible GL(n+1)-representation space of algebraic curvature tensors in order to translate the Nijenhuis integrability conditions for a Killing tensor into purely algebraic integra…
We give various estimates of the first eigenvalue of the p-Laplace operator on closed Riemannian manifold with integral curvature conditions.
In [17] A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential equations. In this paper we investigate the integrability of the Rapcsák system, consisting of the Rapcsák equations and the homogeneity condition, by using the Spence…
A theorem proves integrability of Fréchet tangent distributions.
problem Integrability of Fréchet tangent distributions on manifolds.
method Introduced Condition W, applied variational approach, used differential forms.
result Existence and uniqueness of maximal foliations.
Develops path integral for spiked tensor model dynamics.
problem Dynamics of spiked tensor model with random initial conditions.
method Path integral approach applied to partial differential equations.
result Large-N saddle point equations dominated by melonic diagrams. A new financial integral constructed without lattice assumptions.
problem Creating a financial integral without assuming a lattice structure.
method Weak no-arbitrage condition and properties of trajectory space.
result Integral not associated with a measure, demonstrating non-lattice integration.
The paper uses Fourier integral theorem for estimating multivariate distributions.
problem Estimating multivariate distributions and conditional distribution functions.
method Natural Monte Carlo and fully nonparametric estimators based on Fourier integral theorem.
result Explicit Monte Carlo estimators without estimated covariance matrix.
In this note a functorial approach to the integration problem of an LA-groupoid to a double Lie groupoid is discussed. To do that, we study the notions of fibred products in the categories of Lie groupoids and Lie algebroids, giving necessary and sufficient conditions for the existence of such. In particular, it turns …
Let G be a Lie groupoid with Lie algebroid g. It is known that, unlike in the case of Lie groups, not every subalgebroid of g can be integrated by a subgroupoid of G. In this paper we study conditions on the invariant foliation defined by a given subalgebroid under which such an integration is possible. We also conside…
We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distingu…
We study conformally flat surfaces with prescribed Gaussian curvature, described by solutions u of the PDE: Δu(x)+K(x)exp(2u(x))=0, with K(x) the Gauss curvature function at $x\in\RR^2$. We assume that the integral curvature is finite. For radially symmetric K we introduce the notion of a least integrally curv…
The study finds conditions for quaternionic structures on symmetric spaces.
problem Conditions for quaternionic structures on symmetric spaces.
method Analysis of Lie group actions and representations.
result Symmetric spaces have invariant quaternionic structures under specific conditions.
It is shown that a simple Lie group G (=SL2) can be locally characterised by an integrability condition on an Aut(g) structure on the tangent bundle, where Aut(g) is the automorphism group of the Lie algebra of G. The integrability condition is t…
Along a Ricci flow solution on a closed manifold, we show that if Ricci curvature is uniformly bounded from below, then a scalar curvature integral bound is enough to extend flow. Moreover, this integral bound condition is optimal in some sense.
Study short-time existence of Ricci-DeTurck flow from rough metrics with Morrey-type integrability.
problem Short-time existence of Ricci-DeTurck flow from rough metrics with specific integrability condition.
method Rough existence theory, preservation and improvement of scalar curvature bounds.
result Preservation and improvement of distributional scalar curvature lower bounds under certain conditions.
Characterizes a class of almost Hermitian 4-manifolds using integral identities.
problem Global characterization of almost Hermitian 4-manifolds.
method Using an integral identity from Sekigawa's work, proving a uniqueness result on Lie algebras.
result Global characterization of the class AH1 of almost Hermitian 4-manifolds. Paper derives a Reilly type integral formula and applies it to inequalities and eigenvalue problems.
problem Developing a new integral formula and its applications in geometric inequalities and eigenvalue problems.
method Derives a Reilly type integral formula associated with the φ-Laplacian and applies it to inequalities and eigenvalue problems. result Obtains Heintze-Karcher and Minkowski type inequalities, and eigenvalue relationships.
In this paper we interpret the integrability of the Dirac structures on some Hilbert C*-modules in terms of an automorphism group. This is the group of orthogonal transformations on the Hilbert C*-module of sections of a Hermitian vector bundle over an smooth manifold M. Some topological properties of the group of inte…
The paper analyzes how grid cells perform path integration and learns hexagon grid patterns.
problem Understanding how grid cells perform path integration calculations.
method Theoretical analysis of a general representation model of path integration by grid cells, identifying group representation and isotropic scaling conditions.
result The learned model of hexagon grid patterns is capable of accurate long distance path integration.
For every adapted, càglàd process (strategy) G and typical càdlàg price paths whose jumps satisfy some mild growth condition we define integral G⋅S as a limit of simple integrals.
The paper bounds eigenvalues and integrals of eigenfunctions on hyperbolic manifolds.
problem Eigenvalues and integrals of eigenfunctions on compact hyperbolic manifolds.
method Spectral decompositions and consistency conditions derived from quadruple overlap integrals.
result Upper bounds on Laplacian eigenvalues and triple overlap integrals.
Constructs Lie groupoid integrating elliptic tangent bundles and Poisson structures.
problem Existence and integration of elliptic tangent bundles and Poisson structures.
method Explicit construction of Lie groupoids and local models for symplectic integration.
result Necessary and sufficient topological condition for integration of elliptic tangent bundles.
This paper explores integrability conditions for generalized metrics and structures on manifolds.
problem Investigating integrability conditions for generalized metrics and structures on manifolds.
method Considered two notions of integrability: Courant bracket and connection-induced bracket. Provided sufficient criteria for integrability.
result Sufficient criteria for integrability of generalized metrics and structures are formulated.
Study of geometric structures on manifolds, focusing on integrability conditions.
problem Understanding the integrability of specific geometric structures.
method Analysis of algebraic types, intrinsic torsions, and distinguished connections.
result Presented first-order integrability conditions and geometric interpretations.
Paper extends Poincaré's work to stochastic differential equations.
problem Existence of first integrals in stochastic differential equations.
method Introduce two definitions of local first integrals for SDEs.
result Stochastic version of Poincaré non-integrability theorem.
We study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to some (pseudo)-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provi…
Analyzes L2-harmonic forms on curved manifolds, proving integrability conditions.
problem Analyzing integrability of L2-harmonic forms on curved manifolds. method Established L∞-estimate via Moser iteration, proved vanishing of integrable forms. result Proves that L2-harmonic forms on non-positively curved manifolds are integrable if and only if they vanish. Classifies 3D F-manifolds with or without Euler fields.
problem Local classification of 3D F-manifolds.
method Integrability condition on multiplication in holomorphic tangent bundle.
result Local classification of 3D F-manifolds.
We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically, we show that such a solution can be approximated by integrals over finite-dimens…
Establishes a link between risk measures and uniform integrability in finance.
problem Understanding uniform integrability in the context of financial risk measures.
method Introduces the folding score of distortion risk measures to study uniform integrability directly with gains and losses.
result Obtains three sets of equivalent conditions for uniform integrability involving coherent risk measures.
We prove a sharp Zhong-Yang type eigenvalue lower bound for closed Riemannian manifolds with control on integral Ricci curvature.
The paper derives upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.
problem Finding upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.
method Using spectral decompositions and consistency conditions derived from quadruple overlap integrals in terms of triple overlap integrals.
result Derives upper bounds on eigenvalues, nearly saturated by the Bolza surface.
Study on smoothness of solutions to nonlinear equations on Riemannian manifolds.
problem Smoothness of solutions to nonlinear equations with Neumann boundary conditions on Riemannian manifolds.
method Integral refinement of Bochner's identity.
result Semilinear Calderón-Zygmund type results on Sobolev regularity.
Paper extends rigidity and vanishing results for totally real submanifolds under Lp-integrable conditions.
problem Rigidity and vanishing properties of totally real submanifolds in complex space forms.
method Extends results by Cuong et al. to a broader range of p-integrable conditions. result Extends the range of p for rigidity and vanishing results. The paper improves curvature estimates for Ricci flow solutions with bounded scalar curvature.
problem Proving curvature estimates for Ricci flow solutions with bounded scalar curvature.
method Localised weighted curvature integral estimates for solutions to Ricci flow.
result Integral curvature estimates imply a uniform bound on the spatial L2 norm of the Riemannian curvature tensor. Quantitative Sobolev extensions lead to Neumann heat kernel bounds.
problem Bounding Neumann heat kernels for domains with integral Ricci curvature.
method Quantitative Sobolev extension operators and Neumann heat kernel estimates.
result Uniform bounds on Neumann heat kernels and eigenvalues.
The anomaly flow on a complex 3-fold is studied with integral Shi-type estimates and long-time existence conditions.
problem Long-time existence of the anomaly flow on a compact complex 3-fold.
method Integral Shi-type estimates adapted from integration-by-parts arguments, with a smallness condition on the slope parameter.
result Long-time existence of the anomaly flow on a compact complex 3-fold under a smallness condition on the slope parameter.
A symplectic integration of a Poisson manifold (M,Λ) is a symplectic groupoid (Γ,η) which realizes the given Poisson manifold, i.e. such that the space of units Γ0 with the induced Poisson structure Λ0 is isomorphic to (M,Λ). This notion was introduced by A. Weinstein in order to quantize Poisson manifolds …
The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is…
A new method calculates fractional moments using the moment-generating function.
problem Computing fractional moments from probability densities.
method Integral framework based on moment-generating function.
result Exact integral expressions for various types of moments.