The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.
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48 results for “local sphericality”
Study local features of decorated representation spaces for spherical surfaces.
problem Local structure of moduli space of spherical surfaces with conical points.
method Analysis of decorated representation spaces of fundamental groups in SU(2).
result Smooth locus of decorated representation spaces is dense and connected.
Solution to qc Yamabe problem on non-spherical quaternionic contact manifolds.
problem qc Yamabe problem on non-spherical quaternionic contact manifolds
method Existence of qc conformal structure with constant qc scalar curvature proved on compact non-locally spherical qc manifolds
result Existence of qc conformal structure with constant qc scalar curvature on compact non-locally spherical qc manifolds
Local rigidity shown for certain spherical conical metrics.
problem Deformation of spherical conical metrics with cone angles > 2π.
method Synthetic geometry approach.
result Local rigidity in the choice of cone positions for a specific family of metrics.
Paper develops invariants for spherical curves using chord diagrams.
problem Developing invariants for spherical curves under local moves.
method Using based chord diagrams and local moves from Reidemeister moves.
result Invariants include both classical and new spherical curve invariants.
Locally classifies 4D spherical symmetric Finsler spaces.
problem Classifying 4D spherical symmetric Finsler spaces.
method Local classification of pseudo-Finsler Berwald structures.
result Six classes of non-Riemannian SO(3)-symmetric pseudo-Finsler Berwald functions.
Spherically symmetric metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a spherically symmetric metric on R^n. In this paper, we study spherically symmetric metrics with constant Ricci curvature and constant flag curvature.
Study calculates eigenvalues and eigenfunctions for spherical triangles and finds fundamental gap behavior.
problem Understanding eigenvalues and gaps in spherical triangles.
method Explicit computation of Dirichlet eigenvalues and eigenfunctions for spherical lunes and triangles.
result Fundamental gap of spherical triangles increases as the angle of the lune decreases.
We provide a direct proof for the positivity of Chen-Nester-Tung quasi-local energy with analytic reference in spherical symmetry. A hoop-type theorem for this energy is also established. Finally, the relation between Chen-Nester-Tung and Brown-York quasi-local energies will be discussed.
Proves local existence and extension principle for Einstein Yang--Mills system with spherical symmetry.
problem Local existence and stability of the spherically symmetric Einstein Yang--Mills system.
method Employed an -based method to prove local existence and establish an extension principle.
result Established local existence and extension principle for the SSEYM with data.
DELIMIT PyTorch enhances deep learning for diffusion imaging.
problem Applying deep learning to spherical diffusion imaging data.
method Added spherical harmonic interpolation and local convolution layers to PyTorch.
result Deep learning can now be applied conveniently to diffusion imaging data.
Paper finds configurations for spherical curves with reductivity four and constructs a reduced curve without certain types of polygons.
problem Unknown configurations for spherical curves with reductivity four and reduced curves without specific polygon types.
method Focused on 5-gons to find unavoidable sets for spherical curves with reductivity four. Constructed a reduced spherical curve without certain types of polygons.
result Found configurations for spherical curves with reductivity four and constructed a reduced curve without specific polygon types.
On a class of Kato manifoldsmath.AG
Study of Kato manifolds and their locally conformally Kähler properties.
problem Characterize Kato manifolds and their locally conformally Kähler metrics.
method Revisit Brunella's proof and construct new examples of Kato manifolds.
result Found a class of Kato manifolds that admit locally conformally Kähler metrics and another class that do not.
Study counts sub-chord diagrams to classify spherical curves.
problem Classifying spherical curves using chord diagrams.
method Counting sub-chord diagrams under specific moves.
result New invariant classifies prime reduced spherical curves.
Two spherical and flat periscopes are analyzed in multi-dimensional space.
problem Understanding the wave fronts of periscopes in various dimensions.
method Local diffeomorphisms of wave fronts induced by 2-mirror systems are described.
result Local diffeomorphisms of wave fronts are characterized for spherical and flat periscopes.
Study shows closed Bach-flat manifolds with positive scalar curvature are locally spherical.
problem Characterizing closed Bach-flat manifolds with positive scalar curvature.
method Applied a different method to show local sphericality compared to previous complete non-compact cases.
result Closed Bach-flat manifolds with positive scalar curvature are locally spherical.
Study spherical conic metrics on Riemann surfaces with isolated singularities.
problem Existence and deformation theory of spherical conic metrics.
method Extended configuration families of simple divisors and Friedrichs extension of the Laplacian.
result Smooth local moduli space of solutions possible when 2 lies in the spectrum of the Laplacian.
We show that every Kato surface (or surface with a global spherical shell) admits a locally conformally Kaehler metric.
Flow preserves isoperimetric ratio for immersed surfaces.
problem Preserving isoperimetric ratio in Willmore flow.
method Non-local -gradient flow for Willmore energy.
result Long-time existence and convergence for spherical initial data.
Spherical Plateau problem studies minimal surfaces in quotients of spheres.
problem Minimal surfaces in quotients of spheres.
method Metric currents, barycenter map method.
result Intrinsic uniqueness of solutions for negatively curved manifolds.
Proves a new Penrose inequality for static spacetimes.
problem Establishing a lower bound on mass using area and static references.
method Develops a new quasi-local Penrose inequality for spherically symmetric static spacetimes.
result Proves a quasi-local Penrose inequality for any spherically symmetric static spacetime.
Characterizes conical angles for metrics with dihedral symmetry.
problem Understanding metrics with specific symmetry properties.
method Using recent results on local invariants of quadratic differentials.
result Complete characterization of conical angles for dihedral spherical metrics.
The paper studies surfaces with spherical curvature lines and their generation by constrained elastic curves.
problem Understanding surfaces with spherical curvature lines and their generation mechanisms.
method The approach involves Lie sphere transformations, Legendre curves, and polynomial conserved quantities of connections.
result Lie applicable surfaces with exactly one family of spherical curvature lines are generated by the lift of constrained elastic curves.
Builds geometric structures for algebraic groups over real closed fields.
problem Characterizing and decomposing algebraic groups over specific valued fields.
method Real algebraic geometry to construct and analyze affine buildings.
result Computed stabilizers and obtained group decompositions.
We consider the class of differential equations that describe pseudo-spherical surfaces of the form and given in Chern-Tenenblat \cite{ChernTenenblat} and Rabelo-Tenenblat \cite{RabeloTenenblat90}. We answer the following question: Given a pseudo-spherical surface determine…
Unique solutions found for wave-like decaying null infinity equations.
problem Wave-like decaying null infinity equations with spherically symmetric Einstein-scalar-field.
method Local and global unique solutions for small initial data.
result Sharp decaying condition for unique solutions.
Proves inequality for special 3D shapes, generalizing to non-symmetric ones.
problem Proving a mathematical inequality for specific 3D shapes.
method Operator theoretic approach combined with spherical function decomposition.
result Generalized inequality for non-symmetric bodies of revolution.
The class of differential equations describing pseudo-spherical surfaces, first introduced by Chern and Tenenblat [3], is characterized by the property that to each solution of a differential equation, within the class, there corresponds a 2-dimensional Riemannian metric of curvature equal to . The class of differe…
Study analyzes spectral properties on specific geometric spaces.
problem Investigates spectral analysis on standard locally homogeneous spaces.
method Uses branching laws and invariant differential operators on spherical homogeneous spaces.
result Proves essential self-adjointness and infinite point spectrum for certain spaces.
Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flowmath.DG
Study shows how curved surfaces evolve smoothly to spherical shapes.
problem Evolution of curved surfaces with capillary boundaries.
method Volume-preserving curvature flow with power mean curvature speed.
result Convex initial hypersurfaces evolve to spherical caps over time.
Study -invariants for spherical 3-manifolds via -homology equivalences.
problem Computing -invariants for spherical 3-manifolds via -homology equivalences.
method Using Bott and Cattaneo's -invariants, defined by integrals over configuration spaces with local systems, and representation theory of finite groups.
result Computed upper bounds for dimensions of spaces spanned by -invariants and finite type invariants.
A spherical set is called convex if for every pair of its points there is at least one minimal geodesic segment that joins these points and lies in the set. We prove that for n >= 3 a complete locally-convex (topological) immersion of a connected (n-1)-manifold into the n-sphere is a surjection onto the boundary of a c…
We show that a compact length space is polyhedral if a small spherical neighborhood of any point is conic.
Estimates spherical functions on SL(3,R) improving previous results.
problem Estimating spherical functions on SL(3,R) with uniform decay.
method Estimates spherical functions using the method of stationary phase and classifies singularities.
result Improves previous results by removing restrictions on group parameter.
We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable positivity assumption and for torsion-free fundamental groups they are still diff…
We prove global rigidity for compact hyperbolic and spherical cone-3-manifolds with cone-angles (which are not Seifert fibered in the spherical case), furthermore for a class of hyperbolic cone-3-manifolds of finite volume with cone-angles , possibly with boundary consisting of totally geodesic hyperbo…
New equations for pseudo-spherical surfaces found, with unique isometric immersions.
problem Finding isometric immersions for pseudo-spherical surfaces described by k-th order evolution equations.
method Investigating the relationship between pseudo-spherical surfaces and k-th order evolution equations, proving the existence of unique isometric immersions.
result There is only one type of k-th order evolution equations that admit local isometric immersions, with universal coefficients of the second fundamental form.
String-net models explore non-spherical fusion categories, revealing new spin structures and representations.
problem Investigating string-net models in non-spherical fusion categories.
method String-net models associate vector spaces to surfaces in terms of graphs decorated by objects and morphisms of a pivotal fusion category.
result String-net spaces count r-spin structures and carry representations of the mapping class group.
Rigidity results are obtained for Riemannian -manifolds with and spherical rank at least . Conjecturally, all such manifolds are locally isometric to a round sphere or complex projective space with the (symmetric) Fubini--Study metric. This conjecture is verified in all odd dimensions, for …
New method uses spherical convolutional Wasserstein distance to validate climate models.
problem Ensuring the accuracy of global climate models.
method Spherical convolutional Wasserstein distance to measure model differences.
result Phase 6 models show modest improvements in realistic climatologies.
Paper resolves decades-old problem about -spectra.
problem Identifying -spectra local information with geometric data.
method Proved equivalence of -orientations and characteristic classes.
result Levitt-Ranicki's theory equivalent to Brumfiel-Morgan's classes.
Novikov equation symmetries, solutions, and pseudo-spherical surfaces studied.
problem Analyzing geometrically integrable Novikov equation properties.
method Lie symmetries, group-invariant solutions, conservation laws, unique continuation, pseudo-spherical surfaces.
result Classification of invariant solutions and existence of analytic metrics for pseudo-spherical surfaces.
We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie group. This applies in particular to smooth, projective spherical varieties.
Study of caustics in Einstein-dust system, showing spacetime singularities and diverging curvature.
problem Understanding caustics and singularities in the Einstein-dust system.
method Established local existence result for spherically symmetric spacetimes containing caustics, constructed from solutions to a PDE problem.
result Obtained spherically symmetric spacetimes with diverging curvature and singular boundary.
P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all harmonic morphisms from any three-dimensional Euclidean and spherical space form to a…
The paper examines gravitational singularities in spacetimes and proves inextendibility.
problem Investigating gravitational singularities in spacetimes.
method Analyzing local holonomy and using it to prove inextendibility.
result Proves the -inextendibility of certain spacetimes.
Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundarymath.DG
Paper solves inequalities for capillary hypersurfaces in half-spaces.
problem Finding inequalities for convex capillary hypersurfaces in half-spaces.
method Introduced quermassintegrals and constructed a new locally constrained curvature flow to prove convergence to spherical caps.
result Obtained Alexandrov-Fenchel inequalities for convex capillary hypersurfaces.
We compute the Szego kernel of the unit circle bundle of a negative line bundle dual to a regular quantum line bundle over a compact Kaehler manifold. As a corollary we provide an infinite family of smoothly bounded strictly pseudoconvex domains on complex manifolds (disk bundles over homogeneous Hodge manifolds) for w…