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.
Researchers propose a new approach to the Hopf problem for aspherical varieties.
Study representation varieties of twisted Hopf links using combinatorial and Hodge theory.
Uniformly elliptic Weingarten spheres in S2xR are congruent to a canonical example.
We prove that a necessary condition for the existence of the remaining problem in the harmonic Hopf construction is also sufficient. We also give some topological applications based on our result.
Paper constructs Hopf real hypersurfaces in complex hyperbolic space.
Solves an old problem by showing round spheres are the only compact surfaces with specific curvature properties.
Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my earlier paper on extension of holomorphic geometric structures on complex manifolds. We use this result to classify th…
Authors show that genus defects of Hopf arborescent links are decidable.
Minimal diffeomorphisms extend uniquely with Hopf differential.
Paper analyzes a new Hopf-Lax semigroup in metric spaces.
Symmetric hypersurfaces with constant mean curvature are spheres.
The Lax-Hopf formula simplifies the value function of an intertemporal optimization (infinite dimensional) problem associated with a convex transaction-cost function which depends only on the transactions (velocities) of a commodity evolution: it states that the value function is equal to the marginal fonction of a fin…
This short note serves as a historical introduction to the Hopf problem: "Does there exist a complex structure on ?" This unsolved mathematical question was the subject of the Conference "MAM 1 (Non-)Existence of Complex Structures on ", which took place at Philipps-Universität Marburg, Germany, between M…
We introduce a method, based on the Poincare-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of Hopf's uniqu…
Non-linear Hopf manifolds can be embedded into linear ones and admit LCK metrics.
Proves a 1930s Hopf conjecture about positive curvature manifolds.
Find first (0,2) mirror symmetry examples on Hopf surfaces.
New algorithm solves Schrödinger bridge problem with mismatched channels.
Analyses cohomology relations for moving frames and coframes.
In this work, we study the stability of Hopf vector fields on Lorentzian Berger spheres as critical points of the energy, the volume and the generalized energy. In order to do so, we construct a family of vector fields using the simultaneous eigenfunctions of the Laplacian and of the vertical Laplacian of the sphere. T…
We associate to each infinite primitive Lie pseudogroup a Hopf algebra of `transverse symmetries', by refining a procedure due to Connes and the first author in the case of the general pseudogroup. The affiliated Hopf algebra can be viewed as a `quantum group' counterpart of the infinite-dimensional primitive Lie algeb…
Automorphism groups of Hopf manifolds are finite and have a bounded order.
Here we study geodesics connecting two given points on odd-dimensional spheres respecting the Hopf fibration. This geodesic boundary value problem is completely solved in the case of 3-dimensional sphere and some partial results are obtained in the general case. The Carnot-Carathéodory distance is calculated. We also p…
In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a very partial answer. We write this paper to call attention to the problem.
Algorithm calculates Hopf invariant for simplicial mappings.
We refine the cyclic cohomological apparatus for computing the Hopf cyclic cohomology of the Hopf algebras associated to infinite primitive Cartan-Lie pseudogroups, and for the transfer of their characteristic classes to foliations. The main novel feature is the precise identification as a Hopf cyclic complex of the im…
Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.
New examples of real hypersurfaces found in complex hyperbolic quadrics.
Stable approach solves equivariant Hopf theorem for G-manifolds.
Analyzes properties of Hopf manifolds from analytic and metric perspectives.
We present a geometric approach, in the spirit of the Chern-Weil theory, for constructing cocycles representing the classes of the Hopf cyclic cohomology of the Hopf algebra H(n) relative to GL(n, R). This provides an explicit description of the universal Hopf cyclic Chern classes, which complements our earlier geometr…
Classifies Legendrian Hopf links in lens spaces.
The Hopf invariant is linked to null-homotopy properties of maps.
In this note we study logarithmic transformations in the sense of differential topology on two fibers of the Hopf surface. It is known that such transformations are susceptible to yield exotic smooth structures on four-manifolds. We will show here that this is not the case for the Hopf surface, all integer homology Hop…
Solves an Arnold trivium problem using calculus and topology.
We present the solution of a longstanding internal problem of noncommutative geometry, namely the computation of the index of a transversally elliptic operator on an arbitrary foliation. The new and crucial ingredient is a certain Hopf algebra associated to the transverse frame bundle. Its cyclic cohomology is defined …
We construct a Hopf action, with an invariant trace, of a bicrossed product Hopf algebra $\cH=\big( \cU(\Fg_1) \acr \cR(G_2) \big)^{\cop}$ constructed from a matched pair of Lie groups and , on a convolution algebra $\cA=C_c^{\ify}(G_1)\rtimes G_2^δ$. We give an explicit way to construct Hopf cyclic cohomolo…
Proves NP and co-NP status for knot core recognition in solid torus.
The paper establishes a version of the Hopf boundary point lemma for sections of a vector bundle over a manifold with boundary. This result may be viewed as a counterpart to the tensor maximum principle obtained by R. Hamilton in 1986. Potential applications include the study of various geometric flows and the construc…
The goal of this paper is to describe Zermelo's navigation problem on Riemannian manifolds as a time-optimal control problem and give an efficient method in order to evaluate its control curvature. We will show that up to change the Riemannian metric on the manifold the control curvature of Zermelo's problem has a simp…
Optimizes the conformal capacity of linked curves in .
We wish to attack the problems that H.~Anciaux and K.~Panagiotidou posed in [1], for non-degenerate real hypersurfaces in indefinite complex projective space. We will slightly change these authors' point of view, obtaining cleaner equations for the almost contact metric structure. To make the theory meaningful, we cons…
Generalizes Hopf degree theorem to nontrivial bundles.
We classify nonsingular holomorphic foliations of dimension and codimension one on certain Hopf manifolds. More general, we prove that all nonsingular codimension one distributions on intermediary or generic Hopf manifolds are integrable and has holomorphic integral first. Also, we prove some results about singular hol…
The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.
For a positive Hopf plumbed arborescent Seifert surface , we study the set of Hopf bands , up to homology and up to the action of the monodromy. The classification of Seifert surfaces for which this set is finite is closely related to the classification of finite Coxeter groups.
Clarifies relation for solving control-affine Schrödinger bridge problems.
The Hopf sign conjecture states that a compact Riemannian 2d-manifold M of positive curvature has Euler characteristic X(M)>0 and that in the case of negative curvature X(M) (-1)^d >0. The Hopf product conjecture asks whether a positive curvature metric can exist on product manifolds like S^2 x S^2. By formulating curv…