This paper presents a curvature-free version of the Log(2k-1) Theorem of Anderson, Canary, Culler & Shalen [ACCS96]. It generalizes a result by Hou [Hou01] and its proof is rather straightforward once we know the work by Lim [Lim08] on volume entropy for graphs. As a byproduct we obtain a curvature-free version of the …
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18 results for “curvature-free”
The paper explores curvature-free effects in manifolds with volume growth and ends-counting.
problem Investigating curvature-free effects in manifolds with volume growth and ends-counting.
method Establishing two main theorems about volume growth and ends-counting.
result Proves the existence of smooth bounded mean-concave exhaustion and escaping geodesic lines.
Improved bounds on geodesic lengths in Riemannian surfaces.
problem Finding precise lengths of geodesics in Riemannian surfaces.
method Proved curvature-free linear length bounds on geodesics.
result Length of -shortest geodesic is at most .
We prove curvature-free versions of the celebrated Margulis Lemma. We are interested by both the algebraic aspects and the geometric ones, with however an emphasis on the second and we aim at giving quantitative (computable) estimates of some important invariants. Our goal is to get rid of the pointwise curvature assum…
We give a combinatorial/geometric argument of the classical result that an affine connection, which is both torsion free and curvature free, is locally an affine space.
The paper finds a short graph incompressible in a complex with specific properties.
problem Finding a short graph in a complex with specific properties.
method Analyzing a finite connected 2-complex with a piecewise Riemannian metric and showing the existence of a 2-incompressible graph.
result The existence of a 2-incompressible graph with a length satisfying a curvature-free inequality.
We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank if and only if they are hyperbolic space forms.
New method proves rigidity of minimal hypersurfaces in curved 4-manifolds.
problem Proving rigidity of minimal hypersurfaces in curved 4-manifolds.
method Combining nonnegative 2-intermediate Ricci curvature and strict positivity of scalar curvature, extending Chodosh-Li-Stryker method.
result Rigidity of two-sided free boundary stable minimal hypersurfaces in 4-manifolds with bounded geometry and weakly convex boundary.
No stable minimal submanifolds in certain conformal domains.
problem Stability of minimal submanifolds in conformal domains.
method Analyzing sectional curvatures and boundary convexity.
result No compact stable free boundary minimal submanifolds exist.
Develops a framework for potentials on Lauritzen manifolds using bi-forms.
problem Developing a framework for potentials on Lauritzen manifolds using bi-forms.
method Developing a framework for potentials on Lauritzen manifolds using bi-forms.
result Constructing a canonical contrast bi-form on dually curvature-free Lauritzen manifolds.
Study shows one-dimensional location-scale-shape models are flat in Wasserstein geometry.
problem Investigating curvature in location-scale-shape models under Wasserstein metric.
method Introduced location-scale-shape model and investigated its geometry.
result Location-scale-shape model is intrinsically flat but extrinsically curved in Wasserstein geometry.
The study pinches conditions for constant mean curvature surfaces in convex 3-manifolds.
problem Understanding the topology and geometry of constant mean curvature surfaces with free boundaries in convex 3-manifolds.
method Provided pinching conditions on the traceless second fundamental form to guarantee surface topology.
result The surface is either a disk, annulus, spherical cap, or Delaunay surface under certain conditions.
Given a closed manifold M, we prove the upper bound of (n+d)/2 for the length of a product of systoles that can form a curvature-free lower bound for the total volume of M, in the spirit of M. Gromov's systolic inequalities. Here n is the dimension of M, while d is the is the cohomological dimension of its fundamental …
We study optimal curvature-free inequalities of the type discovered by C. Loewner and M. Gromov, using a generalisation of the Wirtinger inequality for the comass. Using a model for the classifying space BS^3 built inductively out of BS^1, we prove that the symmetric metrics of certain two-point homogeneous manifolds t…
Sharp bounds found on shortest geodesic on punctured spheres.
problem Finding the shortest closed geodesic on punctured spheres.
method Sharp curvature-free upper bounds expressed in terms of area, extremal metrics described.
result Optimal bounds for spheres with up to four ends, extended to larger numbers of punctures.
In this paper we prove the following pointwise and curvature-free estimates on convexity radius, injectivity radius and local behavior of geodesics in a complete Riemannian manifold : 1) the convexity radius of , $\operatorname{conv}(p)\ge \min\{\frac{1}{2}\operatorname{inj}(p),\operatorname{foc}(B_{\operatorname…
A new method using mod n covering improves systolic inequalities.
problem Stable systolic inequalities in Riemannian geometry.
method Mod n covering approach to force nonzero cup products or indices.
result Improved stable two systolic bounds for various manifolds.
TD(0) with Polyak-Ruppert averaging achieves robust and fast convergence rates
problem TD(0) learning under Markovian sampling
method Polyak-Ruppert averaging with a single stepsize
result Simultaneous high-probability convergence guarantees for TD(0) iterates and PR average