arXiv research

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

In this paper, we study generalized constant ratio surfaces in the Euclidean 4-space. We also obtain a classifications of constant slope surfaces.

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…

Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.

A twisted curve in Euclidean 3-space E^3 can be considered as a curve whose position vector can be written as linear combination of its Frenet vectors. In the present study we study the twisted curves of constant ratio in E^3 and characterize such curves in terms of their curvature functions. Further, we obtain some re…

Geodesic flows on surfaces have specific fractional-linear integrals related to constant cross-ratios.

A hypersurface in a Euclidean space $\mathbb{E}^{n+1}$ is said to be a generalized constant ratio (GCR) hypersurface if the tangential part of its position vector is one of its principle directions. In this work, we move the study of generalized constant ratio hypersurfaces started in \cite% {YuFu2014GCRS} into the Min…

Curves in ${\mathbb R}^n$ for which the ratios between two consecutive curvatures are constant are characterized by the fact that their tangent indicatrix is a geodesic in a flat torus. For $n= 3,4$, spherical curves of this kind are also studied and compared with intrinsic helices in the sphere.

A new method achieves optimal uniformity in designs with minimal flexibility.

Paper shows how to embed Möbius bands with many twists and small aspect ratios.

The paper bounds Cheeger ratios of eigenfunctions and their level sets.

Study finds all helical surfaces with a constant ratio of principal curvatures.

We prove that among all constant width bodies of revolution, the minimum of the ratio of the volume to the cubed width is attained by the constant width body obtained by rotation of the Reuleaux triangle about an axis of symmetry.

A simple example shows that losing all money is compatible with a very high Sharpe ratio (as computed after losing all money). However, the only way that the Sharpe ratio can be high while losing money is that there is a period in which all or almost all money is lost. This note explores the best achievable Sharpe and …

Computes constants for cyclic covers of translation surfaces.

A new algorithm detects changes in data with constant cost per iteration.

When trading incurs proportional costs, leverage can scale an asset's return only up to a maximum multiple, which is sensitive to its volatility and liquidity. In a model with one safe and one risky asset, with constant investment opportunities and proportional costs, we find strategies that maximize long term returns …

Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.

The paper proves isoperimetric inequalities in manifolds with small negative Ricci curvature.

The study finds parametrizations for surfaces of revolution with a linear curvature ratio.

In this paper, we mainly study the mean curvature flow in Kähler surfaces with positive holomorphic sectional curvatures. We prove that if the ratio of the maximum and the minimum of the holomorphic sectional curvatures is less than 2, then there exists a positive constant $δ$ depending on the ratio such that $\cosα\ge…

We give asymptotic bounds for the optimal Lipschitz constants for the systole map from the Teichmuller space to the curve complex. We give similar results to those known for closed surfaces in the cases when the genus is fixed or the ratio of genus and punctures is a rational number.

New findings allow infinite mean intensity Hawkes processes to be stable.

On a closed weighted Riemannian manifold with nonnegative Bakry-Émery Ricci curvature, it is shown that the ratio of the $k$-th to first eigenvalues of the weighted Laplacian is dominated by $641k^2$, using an argument via the Cheeger constant. While improving the previous exponential upper bound, the order of $k$ here…

The main result of this paper is: Given any constant C, there is $(ε,k,L)$ such that if a complete, orientable, noncompact odd-dimensional manifold with bounded positive sectional curvature contains a $(ε,k,L)$-neck, then the asymptotic scalar curvature ratio is bigger or equal to C. As a application we proved that the…

This research solves Plateau's problem for CRPC surfaces.

Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wish…

Given $φ$ a pseudo-Anosov map, let $\ell_\mathcal{T}(φ)$ denote the translation length of $φ$ in the Teichmüller space, and let $\ell_\mathcal{C}(φ)$ denote the stable translation length of $φ$ in the curve graph. Gadre--Hironaka--Kent--Leininger showed that, as a function of Euler characteristic $χ(S)$, the minimal po…

The study classifies isometric immersions with specific geometric properties in Riemannian manifolds.

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…

Improved variational inequality algorithms using adaptive step sizes.

Study shows eigenvalue of Hodge Laplacian on coexact 1-forms in hyperbolic 3-manifolds is related to isoperimetric ratio.

Proves Nakai webs have rank 0 or 1, provides examples.

The study proves a new upper bound for isoperimetric ratio in scalar-flat conformal classes.

Empirical study on SGD hyperparameters and adversarial robustness.

Adaptive learning rate improves FTRL's performance in online learning.

This paper defines the pressure metric on the Moduli space of Margulis spacetimes without cusps and shows that it is positive definite on the constant entropy sections. It also demonstrates an identity regarding the variation of the cross-ratios.

We give examples of asymptotically flat three-manifolds $(M,g)$ which admit arbitrarily large constant mean curvature spheres that are far away from the center of the manifold. This resolves a question raised by G. Huisken and S.-T. Yau in 1996. On the other hand, we show that such surfaces cannot exist when $(M,g)$ ha…

Study optimal portfolio strategies with time-varying discount rates.

Modeling financial markets with sandpile model to understand price volatility and arbitrage constraints.

We find an upper bound for the entropy of a systolically extremal surface, in terms of its systole. We combine the upper bound with A. Katok's lower bound in terms of the volume, to obtain a simpler alternative proof of M. Gromov's asymptotic estimate for the optimal systolic ratio of surfaces of large genus. Furthermo…

Efficiently private clustering algorithms with tight approximation ratios.

The paper explores rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space.

Given a quasisymmetric homeomorphism $\varphi$ of the circle, Bonsante and Schlenker proved the existence and uniqueness of the minimal Lagrangian extension $f_\varphi:\mathbb{H}^2\to\mathbb{H}^2$ to the hyperbolic plane. By previous work of the author, its maximal dilatation satisfies $\log K(f_\varphi)\leq C||\varphi…

We highlight the relation between the projective geometries of $n$-dimensional Euclidean, spherical and hyperbolic spaces through the projective models of these spaces in the $n+1$-dimensional Minkowski space, using a cross ratio notion which is proper to each of the three geometries.

We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds. We prove a new lower bound on the competitive ratio of any online algorithm in the setting where the costs are $m$-strong…

The position of the EWS (economy-wide substitution)-ratio vector determines the Rybczynski sign pattern, which expresses the factor endowment--commodity output relationships, and the Stolper-Samuelson sign pattern, which expresses the commodity price--factor price relationships in a three-factor two-good general equili…

Maps preserve distances in non-positively curved spaces.