We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxembourg's construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this construction varies as one changes the family of pseudometrics used…
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48 results for “local construction”
Localized Kasner-like singularities constructed in spacetime.
problem Constructing localized singular solutions to Einstein vacuum equations.
method First order symmetric hyperbolic formulation, adapted orthonormal frame.
result Localized Kasner-like singularities with refined uniqueness and general asymptotic data.
New method calibrates local volatility models to marginal distributions.
problem Calibrating local volatility models to specific marginal distributions.
method Inspired by volatility interpolation, constructs time-homogeneous or continuous local volatility functions.
result Efficient numerical algorithms for constructing local volatility functions.
The existence of negatively curved metrics on locally conformally flat manifolds with boundarymath.DG
Constructs metrics with negative curvature on specific manifold types.
problem Creating negatively curved metrics on locally conformally flat manifolds.
method Using Morse functions to construct conformal metrics.
result Successfully constructs conformal metrics with negative sectional curvature.
New method constructs axial vector fields and defines quasi-local spin-angular momentum.
problem Constructing axial vector fields on Riemannian two-spheres.
method Using centre-of-mass unit sphere reference systems and Lie-propagated unit sphere reference systems.
result Constructive definition of quasi-local spin-angular momentum and balance relations.
Constructs Cartan geometries from automorphism behaviors.
problem Determining Cartan geometries from automorphism local behavior.
method Introduces a construction for Cartan geometries capturing automorphism local behavior.
result The sprawl uniquely characterizes Cartan geometries with equivalent local behavior.
We construct several new classes of isospectral manifolds with different local geometries. After reviewing a theorem by Carolyn Gordon on isospectral torus bundles and presenting certain useful specialized versions (Chapter 1) we apply these tools to construct the first examples of isospectral four-dimensional manifold…
Unified Long-Moody and Katz methods for constructing local systems.
problem Constructing representations of braid groups and local systems.
method Katz-Long-Moody functor unifying Long-Moody and Katz methods.
result Extends Katz algorithm to various topological spaces.
Local examples of singular connections with bounded energy.
problem Constructing singular Hermitian Yang-Mills connections with bounded energy.
method Local construction of singular connections over .
result Number of essential singular points can be arbitrarily large.
Continues work on derived manifolds and symplectic schemes, constructing virtual classes.
problem Constructing virtual fundamental classes for derived manifolds and schemes.
method Cosection localization, reduced virtual fundamental classes, and applications to Donaldson-Thomas theory.
result Virtual fundamental classes for -shifted symplectic derived schemes are consistent with algebraic and differential geometric constructions.
We give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a spray vector field lifting the underlying anchor map. This construction leads to a complete account of local Lie theory and, in particular, to a finite-dimensional p…
Construction of Local Conservation Laws by Generalized Isometric Embeddings of Vector Bundlesmath.DG
This article uses Cartan-Kähler theory to construct local conservation laws from covariantly closed vector valued differential forms, objects that can be given, for example, by harmonic maps between two Riemannian manifolds. We apply the article's main result to construct conservation laws for covariant divergence free…
Constructs a map with prescribed local Lipschitz constants on a subset of a manifold.
problem Creating a Lipschitz map with specific local Lipschitz constants on a subset of a manifold.
method Constructs a Lipschitz map that matches a given map on a subset and has a local Lipschitz constant defined by a continuous function.
result A Lipschitz map can be constructed with a local Lipschitz constant prescribed by a continuous function.
Desingularizes singular foliations with a locally compact groupoid.
problem Handling singularities in foliations.
method Blow-up construction of smooth manifolds and groupoids.
result Locally compact locally Hausdorff groupoid desingularizes singular foliations.
We show that the classical example of a 3-dimensional generalized manifold constructed by van Kampen is another example of not homologically locally connected (i.e. not HLC) space. This space is not locally homeomorphic to any of the compact metrizable 3-dimensional manifolds constructed in our earlier paper wh…
The Chern Character of θ-summable Fredholm Modules over dg Algebras and Localization on Loop Spacemath.KT
We introduce the notion of a {\vartheta}-summable Fredholm module over a locally convex dg algebra Ω and construct its Chern character as a cocycle on the entire cyclic complex of Ω, extending the construction of Jaffe, Lesniewski and Osterwalder to a differential graded setting. Using this Chern character, we prove an…
Construct geometric interpretation of Heston model using group quantization.
problem Geometric interpretation of Heston model
method Lifted local Lie groupoid formulation
result Geometric interpretation of Heston pricing operator and Riccati equations
We generalize the classical study of Alexander polynomials of smooth or PL locally-flat knots to PL knots that are not necessarily locally-flat. We introduce three families of generalized Alexander polynomials and study their properties. For knots with point singularities, we obtain a classification of these polynomial…
New method constructs flat initial data for Einstein's equations.
problem Constructing asymptotically flat initial data for Einstein's equations.
method Explicit solution operators with localization properties.
result Improved decay rate and nontrivial initial data construction.
Totally geodesic subvarieties in moduli space are locally rigid.
problem Understanding rigidity of subvarieties in moduli space.
method General rigidity result for orbifold maps to moduli space.
result Covering constructions and totally geodesic subvarieties are locally rigid.
Understanding the loss surface of neural networks is essential for the design of models with predictable performance and their success in applications. Experimental results suggest that sufficiently deep and wide neural networks are not negatively impacted by suboptimal local minima. Despite recent progress, the reason…
We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an integral criterion and by non-uniqueness of an associated ordinary differential equat…
Bredon has constructed a 2-dimensional compact cohomology manifold which is not homologically locally connected, with respect to the singular homology. In the present paper we construct infinitely many such examples (which are in addition metrizable spaces) in all remaining dimensions .
Global and local blowups of manifolds are proven equivalent.
problem Equivalence of global and local blowups in differential topology.
method Proof of equivalence between global and local constructions of blowups.
result Global and local constructions of blowups are shown to be equivalent.
In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth of size these sets of isospectral manifolds as a function of volume is super-pol…
We construct compactifications of Riemannian locally symmetric spaces arising as quotients by Anosov representations. These compactifications are modeled on generalized Satake compactifications and, in certain cases, on maximal Satake compactifications. We deduce that these Riemannian locally symmetric spaces are topol…
We introduce an elementary way of constructing principal (Z_2)^m-bundles over compact smooth manifolds. In addition, we will define a general notion of locally standard (Z_2)^m-actions on closed manifolds for all m>0, and then give a general way to construct all such (Z_2)^m-actions from the orbit space. Some related t…
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.
We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients of all four-dimensional connected and simply connected solvable Lie groups.
Constructs universal local deformations for curves and differential forms.
problem Local deformations of curves and differential forms under preservation of periods.
method Develops Kuranishi families for pairs of curves and meromorphic 1-forms, focusing on hyperelliptic cases.
result First paper in a series developing a deformation theory for spectral curve data of integrable systems.
Local-to-global principle for Morse actions on symmetric spaces.
problem Recognizing Morse actions on symmetric spaces.
method Equivariant Morse quasiisometric embeddings of trees into symmetric spaces.
result Algorithmic recognizability of Morse actions and construction of Morse Schottky subgroups.
This paper develops a new method for constructing splines on Lie groups using Poisson equation solutions.
problem Existing methods for constructing splines on Lie groups have limitations and assumptions that may not reflect actual curves.
method The paper introduces a new approach using solutions of the Poisson equation on Lie groups to construct splines.
result The new method allows for global splines with arbitrary initial conditions, improving curve reconstruction.
In this paper, we introduce local expressions for discrete Mechanics. To apply our results simultaneously to several interesting cases, we derive these local expressions in the framework of Lie groupoids, following the program proposed by Alan Weinstein in [19]. To do this, we will need some results on the geometry of …
The paper constructs local solutions concentrating near singular points of spinors.
problem Constructing solutions near singular points of spinors.
method Constructs local solutions parameterized by ε, concentrating near singular points.
result Local solutions concentrate in tubular neighborhoods of singular points, converging to original spinors after renormalization.
Study shows certain Lie groups lead to Oeljeklaus-Toma manifolds.
problem Understanding locally conformally Kähler metrics and their relation to Oeljeklaus-Toma manifolds.
method Analyzing solvable Lie groups and their metrics, and relating them to Oeljeklaus-Toma constructions.
result Found a connection between Lie groups, locally conformally Kähler metrics, and Oeljeklaus-Toma manifolds.
New method constructs spacelike data leading to trapped surfaces.
problem Formation of trapped surfaces from spacelike initial data.
method Free data formalism and local existence result.
result Data can be extended to asymptotically flat Cauchy data.
Locally rigid groups from 5-polytopes with Fuchsian ends.
problem Constructing locally rigid right-angled Coxeter groups with Fuchsian ends.
method Constructing a right-angled 5-polytope P and analyzing its right-angled Coxeter groups.
result Locally rigid right-angled Coxeter groups with Fuchsian ends can be constructed.
Construct quaternionic-Kähler metrics from special Kähler manifolds with specific BPS structure variations.
problem Construct quaternionic-Kähler metrics from special Kähler manifolds with mutually local variations of BPS structures.
method Construct quaternionic-Kähler metrics from a conical special Kähler manifold with a certain type of mutually-local variation of BPS structures. Provide global and local explicit formulas for the quaternionic-Kähler metric.
result Construct quaternionic-Kähler metrics that are positive-definite and deform the 1-loop corrected Ferrara-Sabharval metric.
In this work we prove the fact that, for a short time, it is possible to construct a smooth parametrized family of isometric embeddings of an arbitrary smooth parametrized family of Riemannian metrics on a smooth closed manifold into an Euclidean space. In order to prove this statement we work out stability estimates w…
We construct a finitely-presented group such that its Vogel-Levine localization is not transfinitely nilpotent. This answers a problem of J. P. Levine.
Study proves positivity of quasi-local masses in general relativity using spinors.
problem Proving the positivity of quasi-local masses in general relativity.
method Using spinors and solving Dirac equation on compact Riemannian manifolds with boundary conditions.
result Gravitational mass bounded by a spacelike topological 2-sphere is non-negative, vanishing only in Minkowski space.
Let $\CV$ be a vector field distribution on manifold . We give an efficient algorithm for the construction of local coordinates on such that $\CV$ may be locally expressed as some partial prolongation of the contact distribution $\Cal C^{(1)}_q$, on the first order jet bundle of maps from to ,…
Local equivalence found between certain solitons and generalized Kähler-Ricci solitons.
problem Understanding and constructing generalized Kähler-Ricci solitons.
method Establishing local equivalence and extending to complete GKRS under natural conditions.
result Local classification and construction of new examples in all dimensions, especially in four dimensions.
By a construction of Berstein and Edmonds every proper branched cover f between manifolds is a factor of a branched covering orbit map from a locally connected and locally compact Hausdorff space called the monodromy space of f to the target manifold. For proper branched covers between 2-manifolds the monodromy space i…
Croke and Kleiner constructed two homeomorphic locally CAT(0) complexes whose universal covers have visual boundaries that are not homeomorphic. We construct two homeomorphic locally CAT(0) complexes so that the visual boundary of one universal cover contains a nonplanar graph, while the visual boundary of the other do…
Constructs initial data for Einstein vacuum equations involving multiple localized gravitational sources.
problem Modeling the interaction of distant gravitational systems in general relativity.
method Time-symmetric initial data construction using gluing schemes and localized sources.
result Produces initial data sets with finite ADM mass and multiple Einstein-Rosen bridges.
New parametrizations for minimal timelike surfaces discovered.
problem Finding parametrizations for minimal timelike surfaces in specific spaces.
method Derived representation formulas for null curves leading to parametrizations of minimal timelike surfaces.
result Examples of minimal timelike surfaces constructed.
Quantum algorithm improves portfolio construction accuracy.
problem Efficiently constructing portfolios with real-world constraints.
method Sampling-based CVaR Variational Quantum Algorithm (VQA) combined with local-search post-processing.
result Achieved a relative solution error of 0.49% on IBM Heron processors.