arXiv research

Derives Fredholm criteria for isotypical components from a Simonenko principle.

Note establishes a local maximum principle for Ricci flow under curvature conditions.

We explain the meaning of local symmetries in physics.

Local-to-global principle for Morse actions on symmetric spaces.

The paper extends local h-principles to complex structures on Stein manifolds.

We establish the proportionality principle between the Riemannian volume and locally finite simplicial volume for Q-rank 1 locally symmetric spaces covered by products of hyperbolic spaces, giving the first examples for manifolds whose cusp groups are not necessarily amenable. Also, we give a simple direct proof of the…

New principle for supersymmetric localization on Lie groups.

Established concavity principle for curved spaces.

This paper improves a local-to-global principle for Morse quasigeodesics.

New method reveals corners of drum shapes.

Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design for graph signals, lead to …

Book introduces principles of LCK geometry for complex manifold students.

Proves local existence and extension principle for Einstein Yang--Mills system with spherical symmetry.

Study the averaging principle for non-autonomous slow-fast systems and apply it to financial local stochastic volatility models.

Assuming local uniform bounds on the metric for a solution of the Chern-Ricci flow, we establish local Calabi and curvature estimates using the maximum principle.

We prove $h$-principle for locally conformal symplectic foliations and contact foliations on open manifolds. We interpret the result on $h$ principle of contact foliations in terms of the regular Jacobi structures.

Gradients help find global optima in complex functions.

We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectional curvature.

The notion of local equivalence relation on a topological space is generalised to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation of a monodromy principle on the extendibility of local Lie morphisms.

In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(α,β)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to study conformal vector fields of some classes of $(α,β)$ spaces under certain c…

Study curve flows with global forcing terms using a distance comparison principle.

A Euclidean (or hyperbolic) circle packing on a closed triangulated surface with prescribed inversive distance is locally determined by its cone angles. We prove this by applying a variational principle.

This paper presents a locally decoupled network parameter learning with local propagation. Three elements are taken into account: (i) sets of nonlinear transforms that describe the representations at all nodes, (ii) a local objective at each node related to the corresponding local representation goal, and (iii) a local…

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and genera…

This paper formalizes the h-principle and sphere eversion in differential topology.

We investigate the validity of the equivalence principle along paths in gravitational theories based on derivations of the tensor algebra over a differentiable manifold. We prove the existence of local bases, called normal, in which the components of the derivations vanish along arbitrary paths. All such bases are expl…

An assumption-free automatic check of medical images for potentially overseen anomalies would be a valuable assistance for a radiologist. Deep learning and especially Variational Auto-Encoders (VAEs) have shown great potential in the unsupervised learning of data distributions. In principle, this allows for such a chec…

We give a maximum principle proof of interior derivative estimates for the Kähler-Ricci flow, assuming local uniform bounds on the metric.

We build an elementary analytico-geometric theory of Segre chains and their jets.

New boundary condition for Black-Scholes equations in strict local martingale models.

We obtain a local Sobolev constant estimate for integral Ricci curvature, which enables us to extend several important tools such as the maximal principle, the gradient estimate, the heat kernel estimate and the $L^2$ Hessian estimate to manifolds with integral Ricci lower bounds, without the non-collapsing conditions.

Let $A$ be a finite-dimensional local commutative algebra over $R$, $\dim_RA=n$. In this work we consider compact manifolds over $A$, and prove that the real part of an $A$-differentiable function is constant. Also we find estimates for the dimensions of some spaces of 1-form.

The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint connected components. Then we show that each of these connected components, composed …

A new method predicts links better across various networks.

This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds (with boundary and corners), similarly to the toric case, but their associated in…

In this paper, we use the distance comparison principle, first been developed by G. Huisken, to study the spatial curve shortening flow. We have got the result that if the initial curve is the helix, then the local minimum of the ratio of the extrinsic and intrinsic distance is non-decreasing. And we have proved a Gray…

In this paper, based on the local comparison principle in [12], we study the local behavior of the difference of two spacelike graphs in a neighborhood of a second contact point. Then we apply it to the constant mean curvature equation in 3-dimensional Lorentz-Minkowski space $\mathbb{L}^3$ and get the uniqueness of cr…

We study the strong maximum principle for horizontal (p-) mean curvature operator and p-(sub)laplacian operator on subriemannian manifolds including, in particular, Heisenberg groups and Heisenberg cylinders. Under a certain Hormander type condition on vector fields, we show the strong maximum principle holds in higher…

QPLEX learns efficient multi-agent Q-values by enforcing IGM principle.

Study Loday algebroids, prove splitting theorem, and linearize problems.

Unified approach classifies stable and minimal elastic curves.

Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.

We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new p…

In this paper we consider Riemannian manifolds $(M^n,g)$ of dimension $n \geq 5$, with semi-positive $Q$-curvature and non-negative scalar curvature. Under these assumptions we prove $(i)$ the Paneitz operator satisfies a strong maximum principle; $(ii)$ the Paneitz operator is a positive operator; and $(iii)$ its Gree…

Study on Einstein manifolds with specific properties.

Paper studies apparent horizon dynamics and introduces a null comparison principle.

On the ground of origins of the theory of Lie groups and Lie algebras, their (co)adjoint representations, and the Pontryagin maximum principle for the time-optimal problem are given an independent foundation for methods of geodesic vector field to search for normal geodesics of left-invariant (sub-)Finsler metrics on L…

This work investigates fundamental questions related to learning features in convolutional neural networks (CNN). Empirical findings across multiple architectures such as VGG, ResNet, Inception, DenseNet and MobileNet indicate that weights near the center of a filter are larger than weights on the outside. Current regu…