arXiv research

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

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

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

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

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.

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 solves a problem related to scalar curvature and boundary metrics.

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 certain spin manifolds can't meet DEC condition.

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

MaskGAN fills in text blanks more flexibly and effectively.

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

Proves positive mass theorems for specific ALF and ALG manifolds.

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

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

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.

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.

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

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…

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

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.

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…

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…

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 $(Σ,γ)$…

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…

In this thesis we consider a way to construct a rich family of compact Riemann Surfaces in a combinatorial way. Given a 3-regualr graph with orientation, we construct a finite-area hyperbolic Riemann surface by gluing triangles according to the combinatorics of the graph. We then compactify this surface by adding finit…

New method shows some 3D shapes can't be filled in certain ways.

The aim of this short note is to fill in a gap in our earlier paper [16] on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper [15]. We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [13, 23] in the so--called $G-$framework…

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…

Almost forty years ago, C.T.C. Wall systematically analyzed the set of "thickenings" of a finite CW complex. Of the results he obtained, probably the most computationally important is the "suspension theorem," which is an exact sequence relating the n-dimensional thickenings of a finite complex to its (n+1)-dimensional…