A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper evaluates CFL algorithms for handling data heterogeneity in federated learning.
Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for many tasks such as clustering evaluation, consensus clustering, and tracking the temporal evolution of clusters. In p…
Explicit formulas for extrinsic Paneitz operators and Q-curvatures for totally umbilic hypersurfaces.
The extrinsic Bonnet-Myers theorem is proven for positive Ricci curvature manifolds.
The study defines and characterizes extrinsic catenaries in hyperbolic space.
We describe extrinsic hyperspheres and totally geodesic hypersurfaces in manifolds with special holonomy. In particular we prove the nonexistence of extrinsic hyperspheres in quaternion-Kaehler manifolds. We develop a new approach to extrinsic hyperspheres based on the classification of special Killing forms.
We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of arbitrary extrinsic symmetric spaces in pseudo-Euclidean spaces by corresponding …
Having developed a description of indefinite extrinsic symmetric spaces by corresponding infinitesimal objects in the preceding paper we now study the classification problem for these algebraic objects. In most cases the transvection group of an indefinite extrinsic symmetric space is not semisimple, which makes the cl…
Study on ratio of intrinsic to extrinsic metrics and its relation to surface area.
New operators and curvatures derived from embedded manifolds.
Analyzes canonical reductive decomposition of extrinsic homogeneous submanifolds.
In this article we introduce a generalization of the Newton transformation to the case of a system of endomorphisms. We show that it can be used in the context of extrinsic geometry of foliations and distributions yielding new integral formulas containing generalized extrinsic curvatures.
Novel coarse extrinsic curvature for Riemannian submanifolds.
We study infinitesimal semi-simple extrinsic symmetric spaces and give a classification in the symplectic case.
We study the topology of (properly) immersed complete minimal surfaces in Hyperbolic and Euclidean spaces which have finite total extrinsic curvature, using some isoperimetric inequalities satisfied by the extrinsic balls in these surfaces, (see \cite{Pa}). We present an alternative and partially unified proof of…
We prove the energy identity and the no neck property for a sequence of smooth extrinsic polyharmonic maps with bounded total energy.
Extrinsic Geometric Flow (EGF) for a codimension-one foliation has been recently introduced by authors as deformations of Riemannian metrics subject to quantities expressed in terms of its second fundamental form. In the paper we introduce soliton solutions to EGF and study their geometry for totally umbilical foliatio…
In the paper we prove, that extrinsic curvature does not impose restrictions on the topology of a contact structure, except the obvious ones.
Classifies minimal submanifolds in complex hyperbolic spaces.
In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.
The diameter of a disc filling a loop in the universal covering of a Riemannian manifold may be measured extrinsically using the distance function on the ambient space or intrinsically using the induced length metric on the disc. Correspondingly, the diameter of a van Kampen diagram filling a word that represents the i…
We prove that complete submanifolds, on which the Omori-Yau weak maximum principle for the Hessian holds, with low codimension and bounded by cylinders of small radius must have points rich in large positive extrinsic curvature. The lower the codimension is, the richer such points are. The smaller the radius is, the la…
The following Theorem is proved: Let M be an n-dimensional (n>2) submanifold of a Riemannian manifold N. Suppose that through each point p of M there exist two (n-1)-dimensional extrinsic spheres of N, which are contained in M in a neighbourhood of p and are tangent to each other at p. Then M is totally geodesic in N o…
Discretizations of the mean curvature and extrinsic curvature components are constructed on piecewise flat simplicial manifolds, giving approximations for smooth curvature values in a mostly mesh-independent way. These constructions are given in combinatoric form in terms of the extrinsic hinge angles, the intrinsic st…
We obtain an optimal estimate for the extrinsic curvature of an entire minimal graph in $\H^2\times\R$, $\H^2$ the hyperbolic plane.
Derives formulas for extrinsic Paneitz operator and -curvature in general dimensions.
Proves uniqueness of geometric flow in various Riemannian manifolds.
We study, from the extrinsic point of view, the structure at infinity of open submanifolds isometrically immersed in the real space forms of constant sectional curvature . We shall use the decay of the second fundamental form of the the so-called tamed immersions to obtain a description at infinity of the subm…
Paper proves a Penrose inequality in extrinsic geometry.
Paper finds convexity in translating solitons for concave flows.
Improving a result of Eschenburg and Kim we give a criterion for semisimplicity of pseudo-Riemannian extrinsic symmetric spaces in terms of the shape operator with respect to the mean curvature vector.
Study proves inequality for hypersurfaces and shows almost extremals are close to Wulff shape.
Geodesic spheres are the only quasicomplete surfaces in 3-space-forms.
In this article, we give the integrability conditions for the existence of an isometric immersion from an orientable simply connected surface having prescribed Gauss map and positive extrinsic curvature into some unimodular Lie groups. In particular, we discuss the case when the Lie group is the euclidean unit sphere $…
Researchers define residue families and use them to solve singular Yamabe problems.
Unified study of surfaces using Clifford algebras.
Study on biconservative surfaces in 4D hyperbolic space, providing extrinsic descriptions.
New systems of linear PDEs discovered in 3D contact manifolds.
We study deformations of Riemannian metrics on a given manifold equipped with a codimension-one foliation subject to quantities expressed in terms of its second fundamental form. We prove the local existence and uniqueness theorem and estimate the existence time of solutions for some particular cases. The key step of t…
The study characterizes constant curvature manifolds using ruled surfaces.
We show that the extrinsic diameter of immersed flat tori in the 3-sphere is under a certain topological condition for the projection of their asymptotic curves with respect to the Hopf fibration.
Study bounds Neumann and Steklov eigenvalues on manifolds and submanifolds.
Paper proves Hamilton's pinching theorem using mean curvature flow.
We study the volume of extrinsic balls and the capacity of extrinsic annuli in minimal submanifolds which are properly immersed with controlled radial sectional curvatures into an ambient manifold with a pole. The key results are concerned with the comparison of those volumes and capacities with the corresponding entit…
Study improves understanding of submanifold reach in Riemannian geometry.
Develops tensor calculus for submanifolds of arbitrary codimension.
For a compact spin manifold isometrically embedded into Euclidean space, we derive the extrinsic estimates from above and below for eigenvalues of the Dirac operators, which depend on the second fundamental form of the embedding. We also show the bounds of the ratio of the eigenvalues.
We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. We show that if the pinching condion is strong enough with a dependance on the norm of the second foundamental form, then the hypersurface is diffeomorphic and almost isometric to a geodesic hypersphere.