arXiv research

Generalizes nonnegativity result for Brown-York mass using noncompact fill-ins.

Motivated by the quasi-local mass problem in general relativity, we apply the asymptotically flat extensions, constructed by Shi and Tam in the proof of the positivity of the Brown--York mass, to study a fill-in problem of realizing geometric data on a 2-sphere as the boundary of a compact 3-manifold of nonnegative sca…

Study shows no large mean curvature fill-ins for nonnegative scalar curvature.

The paper solves a problem related to scalar curvature and boundary metrics.

In the first part of this paper, we consider the problem of fill-in of nonnegative scalar curvature (NNSC) metrics for a triple of Bartnik data $(Σ,γ,H)$. We prove that given a metric $γ$ on $\mathbf{S}^{n-1}$ ($3\leq n\leq 7$), $(\mathbf{S}^{n-1},γ,H)$ admits no fill-in of NNSC metrics provided the prescribed mean cur…

New rigidity theorems for spin fill-ins with non-negative scalar curvature.

Constructs fill-ins with scalar curvature lower bounds for geometric applications.

Proves Gromov's conjecture on total mean curvature using surgery and positive mass theorems.

Paper discusses quasilocal mass and fill-ins, proving positivity and exploring definitions.

Researchers prove an inequality linking spin manifold fill-ins to hyperspherical radius.

MaskGAN fills in text blanks more flexibly and effectively.

Proves positive mass theorems for specific ALF and ALG manifolds.

We derive new inequalities between the boundary capacity of an asymptotically flat 3-manifold with nonnegative scalar curvature and boundary quantities that relate to quasi-local mass; one relates to Brown--York mass and the other is new. We argue by recasting the setup to the study of mean-convex fill-ins with nonnega…

The paper proves conditions for positive scalar curvature metrics on manifolds with incompressible hypersurfaces.

Study shows certain spin manifolds can't meet DEC condition.

Study bounds total mean curvature of fill-ins with scalar curvature constraints.

This paper improves VAE-based imputation of FX implied volatilities, reducing errors and handling uncertainty.

Study metrics with specific spectral properties to compute Bartnik and Bartnik-Bray masses efficiently.

Paper proves flat 3-manifolds with positive mass have unique isoperimetric surfaces.

We address the problem of surface inpainting, which aims to fill in holes or missing regions on a Riemann surface based on its surface geometry. In practical situation, surfaces obtained from range scanners often have holes where the 3D models are incomplete. In order to analyze the 3D shapes effectively, restoring the…

In this short note, we formulate three problems relating to nonnegative scalar curvature (NNSC) fill-ins. Loosely speaking, the first two problems focus on: When are $(n-1)$-dimensional Bartnik data $\big(Σ_i ^{n-1}, γ_i, H_i\big)$, $i=1,2$, NNSC-cobordant? (i.e., there is an $n$-dimensional compact Riemannian manifold…

Upper bound for total mean curvature of spin fill-ins is proven.

Consider a triple of "Bartnik data" $(Σ, γ,H)$, where $Σ$ is a topological 2-sphere with Riemannian metric $γ$ and positive function $H$. We view Bartnik data as a boundary condition for the problem of finding a compact Riemannian 3-manifold $(Ω,g)$ of nonnegative scalar curvature whose boundary is isometric to $(Σ,γ)$…

In this paper, we extend the T-duality isomorphism by Gualtieri and Cavalcanti, from invariant exact Courant algebroids, to exotic exact Courant algebroids such that the momentum and winding numbers are exchanged, filling in a gap in the literature.

In this paper, we present a new approach to the construction of Einstein metrics by a generalization of Thurston's Dehn filling. In particular in dimension 3, we will obtain an analytic proof of Thurston's result.

Latent variable models can be used to probabilistically "fill-in" missing data entries. The variational autoencoder architecture (Kingma and Welling, 2014; Rezende et al., 2014) includes a "recognition" or "encoder" network that infers the latent variables given the data variables. However, it is not clear how to handl…

In this paper we show that for a Berger metric $\hat{g}$ on $S^3$, the non-positively curved conformally compact Einstein metric on the $4$-ball $B_1(0)$ with $(S^3, [\hat{g}])$ as its conformal infinity is unique up to isometries and it is the metric constructed by Pedersen \cite{Pedersen}. In particular, since in \ci…

Let $S_n$ be a punctured Riemann spheres $\mathbf{S}^2\backslash \{x_1,..., x_n\}$. In this paper, we investigate pseudo-Anosov maps on $S_n$ that are isotopic to the identity on $S_n\cup \{x_n\}$ and have the smallest possible dilatations. We show that those maps cannot be obtained from Thurston's construction (that i…

MaskCycleGAN-VC improves voice conversion without parallel data.

We prove that each overtwisted contact structure has knot types that are represented by infinitely many distinct transverse knots all with the same self-linking number. In some cases, we can even classify all such knots. We also show similar results for Legendrian knots and prove a "folk" result concerning loose transv…

Hybrid methods that utilize both content and rating information are commonly used in many recommender systems. However, most of them use either handcrafted features or the bag-of-words representation as a surrogate for the content information but they are neither effective nor natural enough. To address this problem, w…

A closed totally geodesic surface in the figure eight knot complement remains incompressible in all but finitely many Dehn fillings. In this paper, we show that there is no universal upper bound on the number of such fillings, independent of the surface. This answers a question of Ying-Qing Wu.

Study finds conditions for minimal surfaces in noncompact spaces.

In this note, we fill in a gap in the literature by proving that the Teichmueller modular groups (mapping class groups) are not Poincare duality groups and the complexes of curves of surfaces have infinite homotopy type (i.e. are not homotopy equivalent to a finite CW-complex).

It is well known that certain combinations of configuration space integrals defined by Bott and Taubes produce cohomology classes of spaces of knots. The literature surrounding this important fact, however, is somewhat incomplete and lacking in detail. The aim of this paper is to fill in the gaps as well as summarize t…

We show that the pseudoconcave holes of some naturally arising class of manifolds, called hyperconcave ends, can be filled in, including the case of complex dimension 2 . As a consequence we obtain a stronger version of the compactification theorem of Siu-Yau and extend Nadel's theorems to dimension 2.

New contact manifolds with many fillings found.

Tensor networks improve sequence modeling with efficient sampling and parallelism.

We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all Q-rank one lattices in semisimple groups of R-rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate …

This paper fills in local bounds for Spearman's footrule and Gini's gamma measures of association.

With the large volume of new information created every day, determining the validity of information in a knowledge graph and filling in its missing parts are crucial tasks for many researchers and practitioners. To address this challenge, a number of knowledge graph completion methods have been developed using low-dime…

The paper proves a spacetime positive mass theorem for singular initial data sets.

In this paper we clarify an issue in the knot surgery construction of Fintushel and Stern. Using knot surgery, they construct an infinite number of smooth structures on 4-manifolds satisfying certain conditions, but they do not explicitly work out the circumstances under which two manifolds that arise from their constr…

Paper fills in technical details for Hitchin's self-duality equations proof.

Let $S$ be a Riemann surface of type $(p,n)$ with $3p+n>4$ and $n\geq 1$. Let $α_1,α_2\subset S$ be two simple closed geodesics such that $\{α_1, α_2\}$ fills $S$. It was shown by Thurston that most maps obtained through Dehn twists along $α_1$ and $α_2$ are pseudo-Anosov. Let $a$ be a puncture. In this paper, we study…

For a certain maximal unipotent family of Abelian varieties over the punctured disc, we show that after a base change, one can complete the family over a disc such that the whole degeneration can be simultaneously balanced embedded into a projective space by the theta functions. Then we study the relationship between t…

Study on filling 3D metrics with 4D Poincaré-Einstein structures.

Let X be a compact 4-manifold with boundary. We study the space of hyperkähler triples on X, modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and describe the tangent space in terms of triples of closed anti-self-dual 2-forms. We al…