Related papers: Fat Triangulations and Differential Geometry

We investigate pinched geometries in a two-dimensional Lorentzian model of quantum Regge calculus (QRC) using the tensor renormalization group (TRG) method. A pinched geometry refers to a configuration with an infinitely long temporal…

For closed connected Riemannian spin manifolds an upper estimate of the smallest eigenvalue of the Dirac operator in terms of the hyperspherical radius is proved. When combined with known lower Dirac eigenvalue estimates, this has a number…

In this article it is shown that the equilateral triangle maximizes the Cheeger constant and minimizes the torsional rigidity among shapes having a fixed minimal width. The proof techniques use direct comparisons with simpler shapes,…

This paper is about the influence of Geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, in particular by the study of…

We study Gauss curvature for random Riemannian metrics on a compact surface, lying in a fixed conformal class; our questions are motivated by comparison geometry. Next, analogous questions are considered for the scalar curvature in…

A. Derdzinki [D] gave examples of Riemannian metrics with harmonic curvature and non parallel Ricci tensor on some compact manifolds $(M,g]$ . We examine their existence as well as their number wich naturally depends on the geometry of the…

We consider the problem of preserving weighted Riemannian metrics of positive Bakry-\'Emery Ricci curvature along surgery. We establish two theorems of this type: One for connected sums, and one for surgeries along higher-dimensional…

We consider a 4-dimensional Riemannian manifold M endowed with a right skew-circulant tensor structure S, which is an isometry with respect to the metric g and the fourth power of S is minus identity. We determine a class of manifolds (M,…

We construct bi-Lipschitz embeddings into Euclidean space for manifolds and orbifolds of bounded diameter and curvature. The distortion and dimension of such embeddings is bounded by diameter, curvature and dimension alone. Our results also…

We construct noncommutative `Riemannian manifold' structures on dual quasitriangular Hopf algebras such as $C_q[SU_2]$ with its standard bicovariant differential calculus, using the quantum frame bundle formalism introduced previously. The…

We approach the problem of finding obstructions to curvature distinguished Riemannian metrics by considering Lorentzian metrics to which they are dual in a suitable sense. Obstructions to the latter then yield obstructions to the former.…

The increasing application of deep-learning is accompanied by a shift towards highly non-linear statistical models. In terms of their geometry it is natural to identify these models with Riemannian manifolds. The further analysis of the…

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products…

This paper begins the study of relations between Riemannian geometry and global properties of contact structures on 3-manifolds. In particular we prove an analog of the sphere theorem from Riemannian geometry in the setting of contact…

In the present paper, we introduce bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian submersions. We…

Following P. M. H. Wilson's paper on sectional curvatures of Kahler moduli, we consider a natural Riemannian metric on a hypersurface f=1 in a real vector space, defined using the Hessian of a homogeneous polynomial f. We give examples to…

Fr\'echet regression generalizes linear regression to metric-space-valued responses by defining fitted values as minimizers of weighted Fr\'echet functionals. Since these weights may have mixed signs, the resulting objective is a signed…

We prove several functional and geometric inequalities only assuming the linearity and a quantitative $\mathrm{L}^\infty$-to-Lipschitz smoothing of the heat semigroup in metric-measure spaces. Our results comprise a Buser inequality, a…

This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…

We investigate local and metric geometry of weighted Carnot-Carath\'eodory spaces which are a wide generalization of sub-Riemannian manifolds and arise in nonlinear control theory, subelliptic equations etc. For such spaces the intrinsic…