Gregory R. Chambers

activity

20122023

most citedQuantitative null-cobordism

14 citations · 40 across the 14 of their papers we have counts for

collaborators

21 papers

math.DG2023

On the relative isoperimetric problem for the cube

Gregory R. Chambers, Lawrence Mouillé

In this article, we solve the relative isoperimetric problem in $[0, 1]^{3}$ for orthogonal polyhedra. Up to isometries of the cube or sets of measure $0$ , the minimizers are of the f…

math.CO2022

A note on Kalai's $3^{d}$ Conjecture

Gregory R. Chambers, Elia Portnoy

Suppose that $C$ is a centrally symmetric $d$ -dimensional convex polytope; in 1989 Kalai conjectured that $C$ has at least $3^{d}$ facets. We prove this result if there are $d$ hyper…

math.GT2022

Uryson width and pants decompositions of hyperbolic surfaces

Gregory R. Chambers

Suppose that $M$ is a hyperbolic surface of genus $g$ and with $n$ cusps. Then we can find a pants decomposition of $M$ composed of simple closed geodesics so that each curve is co…

math.DG2022

Geodesic nets on non-compact Riemannian manifolds

Gregory R. Chambers, Yevgeny Liokumovich, Alexander Nabutovsky +1

A geodesic flower is a finite collection of geodesic loops based at the same point $p$ that satisfy the following balancing condition: The sum of all unit tangent vectors to all ge…

math.DG2022

On minimal higher genus fillings

Gregory R. Chambers

In this article, we prove that if $(M, g)$ is a genus $G$ orientable surface with a single boundary component $S^{1}$ , and if $(D, g_{0})$ is a disc such that interior points are connect…

math.FA2020★ 2 cited

A stability result for Riesz potentials in higher dimensions

Almut Burchard, Gregory R. Chambers

We prove a stability estimate, with the optimal quadratic error term, for the Coulomb energy of a set in $R^{n}$ with $n \geq 3$ . This estimate extends to a range of Riesz p…

math.DG2017

Constructing monotone homotopies and sweepouts

Erin Wolf Chambers, Gregory R. Chambers, Arnaud de Mesmay +2

This article investigates when homotopies can be converted to monotone homotopies without increasing the lengths of curves. A monotone homotopy is one which consists of curves whic…

math.DG2017

Area of convex disks

Gregory R. Chambers, Christopher Croke, Yevgeny Liokumovich +1

This paper considers metric balls $B (p, R)$ in two dimensional Riemannian manifolds when $R$ is less than half the convexity radius. We prove that $A r e a (B (p, R)) \geq \frac{8}{π} R^{2}$ .…

math.GT2016★ 7 cited

Quantitative nullhomotopy and rational homotopy type

Gregory R. Chambers, Fedor Manin, Shmuel Weinberger

In \cite{GrOrang}, Gromov asks the following question: given a nullhomotopic map $f : S^{m} \to S^{n}$ of Lipschitz constant $L$ , how does the Lipschitz constant of an optimal nullhomoto…

math.GT2016★ 14 cited

Quantitative null-cobordism

Gregory R. Chambers, Dominic Dotterrer, Fedor Manin +1

For a given null-cobordant Riemannian $n$ -manifold, how does the minimal geometric complexity of a null-cobordism depend on the geometric complexity of the manifold? In [Gro99], Gr…

math.DG2016

Existence of minimal hypersurfaces in complete manifolds of finite volume

Gregory R. Chambers, Yevgeny Liokumovich

We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of…

math.MG2016

A note on the affine-invariant plank problem

Gregory R. Chambers, Lawrence Mouillé

Suppose that $C$ is a bounded, convex subset of $R^{n}$ , and that $P_{1}, \dots, P_{k}$ are planks which cover $C$ in respective directions $v_{1}, \dots, v_{k}$ and with widths $w_…

math.DG2015

Splitting a contraction of a simple curve traversed $m$ times

Gregory R. Chambers, Yevgeny Liokumovich

Suppose that $M$ is a $2$ -dimensional oriented Riemannian manifold, and let $γ$ be a simple closed curve on $M$ . Let $mγ$ denote the curve formed by tracing $γ$ $m$ times. We prov…

math.DS2015★ 4 cited

Ergodic properties of folding maps on spheres

Almut Burchard, Gregory R. Chambers, Anne Dranovski

We consider the trajectories of points on $S^{d - 1}$ under sequences of certain folding maps associated with reflections. The main result characterizes collections of fol…

math.DG2015★ 7 cited

Isoperimetric Regions in $R^{n}$ with density $r^{p}$

Wyatt Boyer, Bryan Brown, Gregory R. Chambers +2

We show that the unique isoperimetric hypersurfaces in $R^{n}$ with density $r^{p}$ for $n \geq 3$ and $p > 0$ are spheres that pass through the origin.

math.DG2014

Optimal sweepouts of a Riemannian 2-sphere

Gregory R. Chambers, Yevgeny Liokumovich

Given a sweepout of a Riemannian 2-sphere which is composed of curves of length less than L, we construct a second sweepout composed of curves of length less than L which are eithe…

math.FA2014★ 6 cited

Geometric stability of the Coulomb energy

Almut Burchard, Gregory R. Chambers

The Coulomb energy of a charge that is uniformly distributed on some set is maximized (among sets of given volume) by balls. It is shown here that near-maximizers are close to ball…

math.DG2013

Proof of the Log-Convex Density Conjecture

Gregory R. Chambers

We completely characterize isoperimetric regions in R^n with density e^h, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isope…

math.DG2013

Monotone homotopies and contracting discs on Riemannian surfaces

Gregory R. Chambers, Regina Rotman

We prove a "gluing" theorem for monotone homotopies; a monotone homotopy is a homotopy through simple contractible closed curves which themselves are pairwise disjoint. We show tha…

math.DG2013

Converting homotopies to isotopies and dividing homotopies in half in an effective way

Gregory R. Chambers, Yevgeny Liokumovich

We prove two theorems about homotopies of curves on 2-dimensional Riemannian manifolds. We show that, for any epsilon > 0, if two simple closed curves are homotopic through curves…

math.MG2012

Perimeter under multiple Steiner symmetrizations

Almut Burchard, Gregory R. Chambers

Steiner symmetrization along n linearly independent directions transforms every compact subset of R^n into a set of finite perimeter.

On the relative isoperimetric problem for the cube

A note on Kalai's 3d Conjecture

Uryson width and pants decompositions of hyperbolic surfaces

Geodesic nets on non-compact Riemannian manifolds

On minimal higher genus fillings

A stability result for Riesz potentials in higher dimensions

Constructing monotone homotopies and sweepouts

Area of convex disks

Quantitative nullhomotopy and rational homotopy type

Quantitative null-cobordism

Existence of minimal hypersurfaces in complete manifolds of finite volume

A note on the affine-invariant plank problem

Splitting a contraction of a simple curve traversed m times

Ergodic properties of folding maps on spheres

Isoperimetric Regions in Rn with density rp

Optimal sweepouts of a Riemannian 2-sphere

Geometric stability of the Coulomb energy

Proof of the Log-Convex Density Conjecture

Monotone homotopies and contracting discs on Riemannian surfaces

Converting homotopies to isotopies and dividing homotopies in half in an effective way

Perimeter under multiple Steiner symmetrizations

A note on Kalai's $3^{d}$ Conjecture

Splitting a contraction of a simple curve traversed $m$ times

Isoperimetric Regions in $R^{n}$ with density $r^{p}$