The paper characterizes geometric infiniteness for convergence group actions using orbit uniform metrics.
problem Characterizing geometric infiniteness for convergence group actions.
method Introducing orbit uniform metrics and proving properties of discrete orbits.
result Characterization of geometric infiniteness in terms of uncountability of non-conical limit points and existence of escaping sequences.
New geometric approach to slow invariant manifolds in dynamical systems.
problem Characterizing slow invariant manifolds in a coordinate-independent manner.
method Exploiting curvature concepts and variational approach in Hamiltonian mechanics.
result Differential geometric definition of slow invariant manifolds proposed.
We characterize geometrically the Lyapunov exponents of a cocycle (of arbitrary rank) with respect to a harmonic current defined on a hyperbolic Riemann surface lamination. Our characterizations are formulated in terms of the expansion rates of the cocycle along geodesic rays.
Extended characterization of RAAGs with zero minimal volume entropy.
problem Characterizing RAAGs with vanishing minimal volume entropy.
method Extended characterization from geometric dimension 2 to higher dimensions.
result Extended characterization of RAAGs with zero minimal volume entropy.
The paper characterizes arithmetic metrics in coarsely geometric settings.
problem Characterizing arithmetic metrics in coarsely geometric settings.
method Using coarse-geometric commensurators and under the Hilbert-Smith conjecture.
result Positive answer in general and unconditional for specific cases.
In this paper we construct the jet geometrical extensions of the KCC-invariants, which characterize a given second-order system of differential equations on the 1-jet space J1(R,M). A generalized theorem of characterization of our jet geometrical KCC-invariants is also presented.
Study geometric step options with jumps, deriving pricing equations and characterizations.
problem Pricing geometric step options in markets with jumps.
method Symmetry and parity relations, partial integro-differential equations, ordinary integro-differential equations.
result Derive semi-analytical pricing results for geometric step options.
Extends Anosov subgroup definitions to more general groups.
problem Characterize subgroups of semisimple Lie groups.
method Relativizes characterizations of Anosov subgroups.
result Proves implications and equivalences between relativized characterizations.
The paper geometrically characterizes graded manifolds and proves the Frobenius theorem.
problem Understanding and characterizing graded manifolds.
method Geometric characterization and Frobenius theorem proof.
result Frobenius theorem proven for graded distributions.
Characterizes hypersurfaces in complex projective and hyperbolic planes.
problem Geometric characterization of hypersurfaces.
method Geometric characterization and partial classifications.
result Characterizes certain hypersurfaces of cohomogeneity one.
Ancient geometric flows of submanifolds are characterized under curvature pinching.
problem Characterizing ancient solutions of geometric flows under curvature constraints.
method Rigidity theorems for ancient solutions of geometric flows of immersed submanifolds.
result Pinching conditions on the second fundamental form characterize the shrinking sphere for mean curvature flow in higher codimensions and certain nonlinear curvature flows of hypersurfaces.
First geometric proof of the flyping theorem.
problem Proving Tait's flyping conjecture.
method Geometric proof using Greene's characterization, Menasco's crossing ball structures, and isotopy/re-plumbing moves.
result First entirely geometric proof of Menasco-Thistlethwaite's flyping theorem.
Study characterizes Einstein manifolds in almost Ricci solitons.
problem Characterizing Einstein manifolds in almost Ricci solitons.
method Geometric dynamics and geometric analysis methods.
result Characterizes Einstein manifolds in the class of complete almost Ricci solitons.
Characterizes Vaisman solvmanifolds and connects them to other geometric structures.
problem Characterizing Vaisman solvmanifolds and their connections to other geometric structures.
method Characterization of unimodular solvable Lie algebras with Vaisman structures in terms of Kähler flat Lie algebras.
result Establishes algebraic restrictions for the existence of Vaisman structures and connects them to other geometric notions.
In this paper we construct some multi-time geometrical extensions of the KCC-invariants, which characterize a given second-order system of PDEs on the 1-jet space J1(T,M). A theorem of characterization of these multi-time geometrical KCC-invariants is given.
Study shows how to deform foliated manifolds with flat leaves, leading to geometric characterization.
problem Deforming foliated manifolds with flat leaves while maintaining curvature bounds.
method Collapsing a manifold with a closed flat regular Riemannian foliation, keeping curvature uniformly bounded.
result For compact, simply connected manifolds, foliations are given by torus actions.
Geometric structures on special manifolds are studied for rigidity.
problem Characterize and prove rigidity of geometric structures on rational homogeneous manifolds.
method Use Cartan geometry to study horospherical varieties and geometric structures modeled on them.
result Geometric structures on smooth projective horospherical varieties of Picard number one are locally equivalent to the standard structure.
This work proposes a geometric approach to identify slow invariant manifolds in dynamical systems.
problem Identifying slow invariant manifolds in multiple time-scale dynamical systems.
method Differential geometric concepts for submanifolds, sectional curvature, flow invariance.
result Necessary condition for slow invariant manifold invariance stated in terms of differential geometry.
Characterizes groups quasi-isometric to RAAGs with geometric actions.
problem Groups quasi-isometric to RAAGs with finite outer automorphism groups.
method Geometric actions on CAT(0) cube complexes with equivariant fibering.
result All such groups admit a geometric action on a CAT(0) cube complex.
The paper characterizes geometrically finite surfaces via geodesic covers.
problem Characterizing geometrically finite surfaces.
method Study of geodesic covers of Fuchsian groups and their metric properties.
result Finiteness of geodesic covers characterizes geometrically finiteness.
The paper characterizes stable cohomotopy groups in codimensions two and three, linking algebraic and geometric perspectives.
problem Characterizing stable cohomotopy groups in specific codimensions.
method Algebraic and geometric approaches, including CW complexes and bordism theory.
result Complete characterizations of stable cohomotopy in codimension two and partial results in codimension three.
Geometrically characterizes virtual nonlinear nonholonomic constraints using symplectic methods.
problem Characterizing virtual nonlinear nonholonomic constraints geometrically.
method Geometric characterization using symplectic structures and Chetaev equations.
result A unique control law exists to satisfy virtual constraints, and closed-loop dynamics are projections of uncontrolled dynamics.
Maps between non-compact surfaces can have geometric kernels under certain conditions.
problem Understanding when maps between non-compact surfaces have geometric kernels.
method Using Brown's proper fundamental group to establish sufficient conditions for geometric kernels.
result Characterization of conjugacy classes in the proper fundamental group and sufficient conditions for geometric kernels.
Study infinite subgroups of higher rank Lie groups, focusing on Anosov subgroups.
problem Understanding properties of Anosov subgroups in higher rank semisimple Lie groups.
method Characterize Anosov subgroups through geometric, coarse geometric, and dynamical viewpoints.
result New equivalent characterizations of Anosov subgroups, capturing rank one behavior.
Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
problem Geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
method Groupoid approach to pseudodifferential calculus, rescaled bundle.
result Rescaled bundle provides geometric characterization to asymptotic pseudodifferential calculus on spinor bundles.
Characterizes homogeneous spaces with geometric structures using connections.
problem Characterizing homogeneous spaces with various geometric structures.
method Using connections to characterize reductive homogeneous spaces.
result Generalizes Ambrose-Singer theorem to non-Riemannian geometries.
Computing PL geometric category in 2D is NP-hard.
problem Determining the PL geometric category of 2D polyhedra.
method Reduction from shellability of 2-complexes, which is known to be NP-hard.
result It is NP-hard to decide whether the PL geometric category of a 2D polyhedron is at most 2.
Characterizes level-set families of harmonic functions without critical points.
problem Understanding level-set families of harmonic functions without critical points.
method Characterization via local differential-geometric condition and construction from geometric data.
result Evolution of gradient of harmonic functions determined by mean curvature of level sets.
Characterizes geometric actions on graphs with flexible stabilizers.
problem Understanding geometric actions on flexible stabilizers.
method Defining generalized fine actions and proving relative quasi-convexity criteria.
result Characterizes Bowditch boundary points in relatively geometric actions.
In this paper, we study face vectors of simplicial posets that are the face posets of cell decompositions of topological manifolds without boundary. We characterize all possible face vectors of simplicial posets whose geometric realizations are homeomorphic to the product of spheres. As a corollary, we obtain the chara…
Study wave front singularities and their geometric properties.
problem Characterize singularities of focal surfaces of wave fronts.
method Characterization through differential geometric properties.
result Relationships between focal surfaces and initial wave fronts' geometric invariants.
We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature of a principal fibre bundle. --Parameterize arbitrage strategies by its holonomy. --Give the Fundamental Theorem of Asset …
The paper characterizes sets with infinite hyperbolic convex hull volume.
problem Characterizing sets with infinite hyperbolic convex hull volume.
method Geometric conditions and self-similar sets.
result Characterizes continua and planar self-similar sets with infinite hyperbolic convex hull volume.
The study characterizes canal hypersurfaces formed by non-null curves with parallel frame in Minkowski space-time.
problem Characterizing canal hypersurfaces in Minkowski space-time.
method Obtained canal hypersurfaces by pseudo hyperspheres or pseudo hyperbolic hyperspheres with parallel timelike normal vector field.
result Gaussian curvature, mean curvature, and principal curvatures of canal hypersurfaces were derived.
We describe the geometric notion of distribution in synthetic terms, utilizing the notion of "first neighbourhood of the diagonal" from algebraic geometry. We characterize involutive distributions in combinatorial terms.
Characterizes surfaces enveloped by rotating cones for CNC machining.
problem Characterizing surfaces enveloped by rotating cones for CNC machining.
method Derives higher-order nonlinear PDEs for enveloping surfaces, including local approximations.
result Characterizations generalize previous work on developable and ruled surfaces.
The exposition has been significantly altered, hopefully improved.
Characterizes Euclidean balls with lower bounded k-th mean curvature.
problem Characterizing convex bodies with lower bounded k-th mean curvature.
method New isoperimetric-type inequality and sharp characterizations.
result Euclidean balls uniquely satisfy the condition.
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible conv…
Uniformly perfect Morse boundaries characterize geometric properties of groups.
problem Characterizing geometric properties of groups using Morse boundaries.
method Introducing and geometrically characterizing uniformly perfect Morse boundaries for proper geodesic metric spaces.
result The Morse boundary of any finitely generated, non-elementary group is uniformly perfect if it is nonempty.
We study a subset of square free positive braids and we give a few algebraic characterizations of them and one geometric characterization: the set of positive braids whose closures are unlinks. We describe canonical forms of these braids and of their conjugacy classes.
Study characterizes geometric properties of QGCR-null submanifolds in cosymplectic manifolds.
problem Characterizing geometric properties of QGCR-null submanifolds in cosymplectic manifolds.
method Characterization through totally umbilical and irrotational properties, and discussion of geodesity conditions.
result Characterizes geometric properties of ascreen QGCR-null submanifolds.
Study spherical Fourier transform on hypergeometric type harmonic manifolds.
problem Spherical Fourier transform on harmonic Hadamard manifolds.
method Representation of spherical functions by Gauss hypergeometric functions.
result Inversion formula, convolution rule, and Plancherel theorem are derived.
In 1996, Huisken-Yau proved that every three-dimensional Riemannian manifold can be uniquely foliated near infinity by stable closed surfaces of constant mean curvature (CMC) if it is asymptotically equal to the (spatial) Schwarzschild solution. Later, their decay assumptions were weakened by Metzger, Huang, Eichmair-M…
The paper extends geometric finiteness to discrete subgroups of negatively pinched Hadamard manifolds.
problem Characterizing geometrically infinite discrete subgroups of negatively pinched Hadamard manifolds.
method Generalizing Bonahon's characterization and proving a theorem of Bishop's extension.
result Every discrete geometrically infinite isometry subgroup has a set of nonconical limit points of cardinality continuum.
Researchers describe Hodge-Laplace spectrum on lens spaces.
problem Characterizing lens spaces based on their form spectra.
method Explicit description and rational function encoding of spectra.
result Geometric characterization of lens spaces with identical spectra.
Geometric argument proves projection theorems in hyperbolic space.
problem Proving projection theorems for hyperbolic space.
method Geometric argument for orthogonal projections.
result Characterization of purely unrectifiable sets in hyperbolic space.
A geometrical interpretation of the G-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of homogeneity, the corresponding inhomogeneity conditions are obtained