Related papers: Yet another sphere eversion
The computation of the effect of a simple monodromy defect in the case of a sphere with twisted boundary conditions is revisited and streamlined using earlier calculations for a similar system. Compact and explicit expressions are found for…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…
In this exploration paper, we design algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete sphere. Such a contraction is a kind of shrinking or reducing process. In our algorithms, we need to…
We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.
In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L^2 inequality of the Weyl tensor and positivity of the Yamabe…
In this note, using some regular triangular tilings of the sphere, the Euclidean plane and the hyperbolic plane, we examine the potential relationship between their discrete Bakry - Emery curvatures and the smooth curvatures of their…
An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…
The X-ray transform on a compact symmetric space M is here inverted by means of an explicit inversion formula. The proof uses the conjugacy of the minimal closed geodesics in M and of the maximally curved totally geodesic spheres in M,…
We consider the motion of an incompressible viscous fluid on a sphere, incorporating the effects of the Coriolis force. We demonstrate that global solutions exist for any divergence-free initial condition with finite kinetic energy.…
We report experimental measurements of the translational and rotational dynamics of a large buoyant sphere in isotropic turbulence. We introduce an efficient method to simultaneously determine the position and (absolute) orientation of a…
We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for…
A weakly deformable droplet impinging on a rigid surface rebounds if the surface is intrinsically hydrophobic or if the gas film trapped underneath the droplet is able to keep the interfaces from touching. A simple, physically motivated…
Real analytic functions on the boundary of the sphere which have separate holomorphic extension along the complex lines through a boundary point have holomorphic extension to the ball. This was proved in a previous preprint by an argument…
We prove conditions under which the total space of the pullback of a sphere fibration over a connected sum is homotopy equivalent to a connected sum with a gyration. Existing results of this type often depend on geometric methods. We…
We develop a new iterative method for finding approximate solutions for spherical bounces associated with the decay of the false vacuum in scalar field theories. The method works for any generic potential in any number of dimensions,…
In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.
Motivated to study the geometry of the exotic spheres constructed in [5], we derive a necessary condition for non-negative sectional curvature in certain total spaces of Riemannian submersions with totally geodesic fibers. In particular, we…
In this paper, we investigate Liu-Xu-Ye-Zhao's conjecture [30] and prove a sharp convergence theorem for the mean curvature flow of arbitrary codimension in spheres which improves the convergence theorem of Baker [2] as well as the…
Parallel to the main results of [13] and [14], which explore the equivalence between prox-regularity, the exterior sphere condition, and $S$-convexity, we present novel characterizations of the $r$-strong convexity property, namely, of the…