arXiv research

Bayesian Gaussian Processes improve exoplanet transit and Hubble constant inference.

Proves closure for specific spacetimes with certain conditions.

Phylogenetic approaches are finding more and more applications outside the field of biology. Astrophysics is no exception since an overwhelming amount of multivariate data has appeared in the last twenty years or so. In particular, the diversification of galaxies throughout the evolution of the Universe quite naturally…

The two-dimensional renormalization group acting as the Ricci flow $Λ\frac{\partial}{\partialΛ} g_{μν} = R_{μν}$ produces a specific 1+3 dimensional space-time metric which describes an expanding universe that starts with a big bang $a \sim t^{\scriptscriptstyle 1/\sqrt3}$ then decelerates until $z=0.2$ then accelerate…

Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to multidimensional data. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. As estimated patterns can be positioned anywhere in signals or images, optimization techniques face…

Observations of astrophysical objects such as galaxies are limited by various sources of random and systematic noise from the sky background, the optical system of the telescope and the detector used to record the data. Conventional deconvolution techniques are limited in their ability to recover features in imaging da…

A proof is given that the maximal Fermi coordinate chart for any comoving observer in a broad class of Robertson-Walker spacetimes consists of all events within the cosmological event horizon, if there is one, or is otherwise global. Exact formulas for the metric coefficients in Fermi coordinates are derived. Sharp uni…

Machine learning detects subhalos in lensed images with high accuracy and low false positives.

Fermat constants fail to fully identify Clairaut constants for certain geodesics on a surface of revolution.

Study proves surfaces with constant curvature are simple shapes.

The paper classifies hypersurfaces in $\mathbb{H}^2 imes\mathbb{H}^2$ with constant curvature.

Study on biconservative hypersurfaces with constant scalar curvature in space forms.

We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the Yamabe constant depends continuously on the Riemannian metric with respect to the fine C^2-topology, and that the Yamabe…

Study CR Yamabe constant and CR structures on manifolds.

The paper studies curves of constant-ratio in pseudo-Galilean space.

The Cheeger constant increases under Ricci flow on spheres.

We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant complex angle with respect to a fixed spacelike plane. This notion is the natural Lo…

The paper defines new constants for $p$-Laplacian on manifolds.

Study classifies 3D self-shrinkers with constant second form norm.

In 1926 S. Nakajima (= A. Matsumura) showed that any convex body in $\R^3$ with constant width, constant brightness, and boundary of class $C^2$ is a ball. We show that the regularity assumption on the boundary is unnecessary, so that balls are the only convex bodies of constant width and brightness.

Study refines Siegel-Veech constants for abelian differentials.

Curves with constant torsion can be deformed arbitrarily.

New upper bound for Cheeger constant of hyperbolic surfaces.

Simplified proof for Cheeger's isoperimetric constant.

Study on isoparametric and constant-curvature hypersurfaces in Finsler spaces.

This paper mixes constant sum and constant product market makers to improve their features.

Ruled surfaces with Ricci metrics use curves of constant torsion.

Paper proves a Liouville theorem for solitons with constant curvature.

Estimates eigenvalues and spectrum for graph substructures using isocapacitary constants.

The paper classifies and constructs rotational surfaces with constant astigmatism in space forms.

A number of results for C$^2$-smooth surfaces of constant width in Euclidean 3-space ${\mathbb{E}}^3$ are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along…

Study on surfaces in Heisenberg group with constant mean curvature.

Defines structure constants for specific geometric structures on Lie groups.

Salkowski \cite{salkow}, one century ago, introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but non-constant curvature (anti-Salkowski curves) in Euclidean 3-space $\e^3$. In this paper, we adapt definition of such curves to ti…

Study constructs closed curves with constant curvature on cylinders and tori.

It is proved that if an AK2-manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then it is a 6-dimensional manifold of constant negative sectional curvature or a Kähler manifold of constant holomorphic sectional curvature.

Every biharmonic Wintgen ideal submanifold in a Riemannian manifold of constant sectional curvature is either minimal or has constant mean curvature.

The study classifies quasi-Einstein manifolds with constant scalar curvature.

Study constant mean curvature surfaces with integrable boundary conditions.

Concrete example of 2-sphere with constant curvature 1 and closed geodesics.

Classifies hypersurfaces with constant curvature in product spaces.

We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension $n\geq 3$. We prove the existence of such conformal metrics in the cases of $n=6,7$ or the manifold is spin and some other remai…

Constructs Kähler metrics with constant scalar curvature on blown-up manifolds.

In this paper, we study generalized constant ratio (GCR) hypersurfaces in Euclidean spaces. We mainly focus on the hypersurfaces in $\mathbb E^4$. First, we deal with $δ(2)$-ideal GCR hypersurfaces. Then, we study on hypersurfaces with constant (first) mean curvature. Finally, we obtain the complete classification of G…

In the work of Ammann, Dahl and Humbert it has turned out that the Yamabe invariant on closed manifolds is a bordism invariant below a certain threshold constant. A similar result holds for a spinorial analogon. These threshold constants are characterized through Yamabe-type equations on products of spheres with rescal…

The study proves constant-curvature analogues of hot spots conjecture for triangles.

The study compares and finds Yamabe constants on warped products.

Open problems on surfaces with boundary and constant mean curvature.