arXiv research

Paper disproves symmetry of stars at infinity in a specific graph.

We define a new version of modified mean curvature flow (MMCF) in hyperbolic space $\mathbb{H}^{n+1}$, which interestingly turns out to be the natural negative $L^2$-gradient flow of the energy functional defined by De Silva and Spruck in \cite{DS09}. We show the existence, uniqueness and convergence of the MMCF of com…

Study of infinity in Teichmüller space using Thurston boundary.

Flow turns star-shaped curves into circles.

Paper establishes an isomorphism between Fukaya category and bordered knot Floer homology.

Paper proves Koszul duality for weighted A-infinity algebras.

We study the evolution of complete non-compact convex hypersurfaces in $\mathbb{R}^{n+1}$ by the inverse mean curvature flow. We establish the long time existence of solutions and provide the characterization of the maximal time of existence in terms of the tangent cone at infinity of the initial hypersurface. Our proo…

Inverse curvature flows shape star-shaped hypersurfaces into spheres.

Constructs Koszul dual algebras for star-shaped diagrams in 3-manifolds.

The derived bracket of a Maurer-Cartan element in a differential graded Lie algebra (DGLA) is well-known to define a differential graded Leibniz algebra. It is also well-known that a Lie infinity morphism between DGLAs maps a Maurer-Cartan element to a Maurer-Cartan element. Given a Lie-infinity morphism, a Maurer-elem…

We consider inverse curvature flows in $\Hh$ with star-shaped initial hypersurfaces and prove that the flows exist for all time, and that the leaves converge to infinity, become strongly convex exponentially fast and also more and more totally umbilic. After an appropriate rescaling the leaves converge in $C^\infty$ to…

The paper challenges the smooth null infinity model by constructing counter-examples and showing non-smoothness of null infinity.

New star-shaped acceptability indexes generalize existing methods.

The paper finds at least four prime closed characteristics on star-shaped hypersurfaces in 8D space.

The paper characterizes law-invariant star-shaped risk measures.

Unified description of p-brane QP-manifolds connects two recent tensor hierarchy descriptions.

Paper characterizes star-shaped risk measures and their properties.

We consider the inverse curvature flows $\dot x=F^{-p}ν$ of closed star-shaped hypersurfaces in Euclidean space in case $0<p\not=1$ and prove that the flow exists for all time and converges to infinity, if $0<p<1$, while in case $p>1$, the flow blows up in finite time, and where we assume the initial hypersurface to be…

The paper characterizes dynamic return and star-shaped risk measures via BSDEs.

We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection introduced by the first author. We establish a necess…

Authors prove an asymptotic expansion for spectral zeta functions on discrete tori.

Given a convex cone in the \emph{prescribed} warped product, we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If those hypersurfaces inside the cone evolve along the inverse mean curvature flow, then, by using the convexity of …

In 1998 Smoczyk [Smo98] showed that, among others, the blowup limits at singularities are convex for the mean curvature flow starting from a closed star-shaped surface in $\mathbf{R}^3$. We prove in this paper that this is true for the mean curvature flow of star-shaped hypersurfaces in $\mathbf{R}^{n+1}$ in arbitrary …

Gaia will obtain astrometry and spectrophotometry for essentially all sources in the sky down to a broad band magnitude limit of G=20, an expected yield of 10^9 stars. Its main scientific objective is to reveal the formation and evolution of our Galaxy through chemo-dynamical analysis. In addition to inferring position…

The study proves that in normal tilings, at least two vertices are required per cell.

Paper introduces a new $G^\star$ regret measure for online convex optimization with smooth losses.

Introduces Star-Shaped DDPMs for non-Gaussian distributions.

New Minkowski inequality for capillary surfaces in half-space.

R. Schwartz's inequality provides an upper bound for the Schwarzian derivative of a parameterization of a circle in the complex plane and on the potential of Hill's equation with coexisting periodic solutions. We prove a discrete version of this inequality and obtain a version of the planar Blaschke-Santalo inequality …

Introduces Star-Shaped deviation measures for risk analysis.

The study shows infinitely many Reeb orbits on star-shaped hypersurfaces with growth rate like prime numbers.

A new definition of umbilic points at infinity for polynomial surfaces.

Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the l…

The paper proves mapping class groups of closed surfaces are simply connected at infinity.

We study connected sum at infinity on smooth, open manifolds. This operation requires a choice of proper ray in each manifold summand. In favorable circumstances, the connected sum at infinity operation is independent of ray choices. For each m at least 3, we construct an infinite family of pairs of m-manifolds on whic…

In the first part of this paper we outline the constructions and properties of Fedosov star product and Berezin-Toeplitz star product. In the second part we outline the basic ideas and recent developments on Yau-Tian-Donaldson conjecture on the existence of Kähler metrics of constant scalar curvature. In the third part…

Algorithm achieves optimal regret for unknown Lipschitz convex losses.

Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.

In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric $Q^m$. It is proved that there exist no Hopf hypersurfaces in $Q^m,m\geq3$, with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on $M$ …

New study finds environment significantly suppresses star formation in galaxies, contrary to previous beliefs.

Classifies star products on Lie algebroid duals and extends to projectable quantizations.

The paper examines mass aspects at future null infinity and limits of quasilocal mass.

Study learns a projection and function in Gaussian models.

Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.

Gradient descent learns over-param neural nets better than NTK.

The paper defines curvature at infinity for flat manifolds.

STAR improves equivariant and invariant representation learning by routing projection heads.

New set-valued star-shaped risk measures introduced for better risk assessment.