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.
Study proposes initial data sets for solving gravitational equations, proving energy estimates.
Unique solutions found for wave-like decaying null infinity equations.
Proves stability of spacetime Penrose inequality for spherical symmetric initial data.
Unique global solutions found for specific initial data.
In this paper, we initiate the study of the instability of naked singularities without symmetries. In a series of papers, Christodoulou proved that naked singularities are not stable in the context of the spherically symmetric Einstein equations coupled with a massless scalar field. We study in this paper the next simp…
The paper studies surfaces with spherical curvature lines and their generation by constrained elastic curves.
Flow preserves isoperimetric ratio for immersed surfaces.
Proves global existence and uniqueness of solutions for Einstein-scalar-field equations.
Study shows directional convergence for neural networks under spherical symmetry.
The rigidity statement of the positive mass theorem asserts that an asymptotically flat initial data set for the Einstein equations with zero ADM mass, and satisfying the dominant energy condition, must arise from an embedding into Minkowski space. In this paper we address the question of what happens when the mass is …
Recently we initiated the study of spherical T-duality for spacetimes that are principal SU(2)-bundles. In this paper, we extend spherical T-duality to spacetimes that are oriented non-principal SU(2)-bundles. There are several interesting new examples in this case and a new phenomenon appearing in the non-principal ca…
The paper explores rigid geometric structures near surfaces with equality in area-charge inequalities.
Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.
Paper resolves spherical curvature flow problem.
We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the Kottler-Schwarzschild-de Sitter metrics in regions of infinite extent. From the purely Rie…
We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initi…
Study perturbs mean curvature flow near non-spherical shrinkers.
Mean curvature flow shows singularities on smooth surfaces.
We show that the causal-future-directed character of the energy-momentum vector of -dimensional asymptotically hyperbolic Riemannian manifolds with spherical conformal infinity, , can be traced back to that of asymptotically Euclidean general-relativistic initial data sets satisfying the dominant energy cond…
The techniques developed by Butscher in arXiv:math/0703469 for constructing constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere by gluing together spherical building blocks are generalized to handle less symmetric initial configurations. The outcome is that the approximately CMC hypersurface obtained by glu…
Convexity properties are preserved under radial transformations in hyperbolic and spherical geometries.
Study on naked singularities without symmetry, forming incomplete future null infinity and singular inner Cauchy horizon.
Constructs initial data leading to apparent horizons and tests Penrose Inequality.
We give general sufficient conditions for the existence of trapped surfaces due to concentration of matter in spherically symmetric initial data sets satisfying the dominant energy condition. These results are novel in that they apply and are meaningful for arbitrary spacelike slices, that is they do not require any au…
Proves Penrose inequality for cohomogeneity one initial data sets.
Study shows how curved surfaces evolve smoothly to spherical shapes.
We prove some related results concerning blow-up solutions for the Jang equation. First: it has been shown that, given an outermost marginally outer trapped surface (MOTS) Σ, there exists a solution to Jang's equation which blows up at Σ. Here we show that in addition, large classes of spherically symmetric initial dat…
Constructs initial data for Einstein equations and estimates Bartnik mass outside time-symmetry.
We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the relevant mass-angular momentum in…
We deform the contact form by the amount of the Tanaka-Webster curvature on a closed spherical three-manifold. We show that if a contact form evolves with free torsion and positive Tanaka-Webster curvature as initial data, then a certain Harnack inequality for the Tanaka-Webster curvature holds.
We introduce certain spherically symmetric singular Ricci solitons and study their stability under the Ricci flow from a dynamical PDE point of view. The solitons in question exist for all dimensions , and all have a point singularity where the curvature blows up; their evolution under the Ricci flow is in sh…
We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as u…
The paper proves smoothness of mean curvature flow for generic initial data in 3D and 4D.
Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003) displays a phase with broken ergodicity and dependence of the macroscopic stationary s…
It is shown that the initial singularities in spatially compact spacetimes with spherical, plane or hyperbolic symmetry admitting a compact constant mean curvature hypersurface are crushing singularities when the matter content of spacetime is described by the Vlasov equation (collisionless matter) or the wave equation…
In this paper we introduce a Guan-Li type volume preserving mean curvature flow for free boundary hypersurfaces in a ball. We give a concept of star-shaped free boundary hypersurfaces in a ball and show that the Guan-Li type mean curvature flow has long time existence and converges to a free boundary spherical cap, pro…
The Willmore flow preserves surface volume, leading to convergence to a sphere.
We consider geometric flows of hypersurfaces expanding by a function of the extrinsic curvature and we show that the homothethic sphere is the unique solution of the flow which converges to a point at the initial time. The result does not require assumptions on the speed other than positivity and monotonicity and it is…
The paper studies a flow for convex capillary hypersurfaces in a ball, proving smooth convergence to a spherical cap.
One way to recognise an object is to study how the echo has been shaped during the interaction with the target. Wideband sonar allows the study of the energy distribution for a large range of frequencies. The frequency distribution contains information about an object, including its inner structure. This information is…
We introduce Tempered Geodesic Markov Chain Monte Carlo (TG-MCMC) algorithm for initializing pose graph optimization problems, arising in various scenarios such as SFM (structure from motion) or SLAM (simultaneous localization and mapping). TG-MCMC is first of its kind as it unites asymptotically global non-convex opti…
PGF kernels analyze spherical data using generalized RBF kernels.
A Steiner chain of length k consists of k circles, tangent to two given non-intersecting circles (the parent circles) and tangent to each other in a cyclic pattern. The Steiner porism states that once a chain of k circles exists, there exists a 1-parameter family of such chains with the same parent circles that can be …
Presented spherical symmetric teleparallel geometry frames and field equations.
We initiate the study of the spherically symmetric Einstein-Klein-Gordon system in the presence of a negative cosmological constant, a model appearing frequently in the context of high-energy physics. Due to the lack of global hyperbolicity of the solutions, the natural formulation of dynamics is that of an initial bou…
Low-entropy surfaces can be flowed into spheres and cylinders.
We continue our study, initiated in our earlier paper, of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier paper of extended configuration families of simple divisors, we study the existence and deformation theory for spherical conic metrics with s…
A new method estimates the number of clusters on spherical data.