Gregory R. Chambers

I am an Associate Professor in the Department of Mathematics at Rice University. Before coming to Rice, I was an L. E. Dickson Instructor at the University of Chicago, and a graduate student at the University of Toronto before that.

My research is in metric geometry and geometric analysis. I am particularly interested in quantitative topology, min-max theory, isoperimetric inequalities, stability estimates for geometric inequalities, and symmetrizations and their applications.

I am a co-organizer of the Geometry Seminar.

Contact Information

Teaching

I am not teaching during the fall 2026 semester.

Students

Publications

  1. Mountain Pass Critical Points of the Volume Constrained Area Functional, with J. Marx-Kuo
    International Mathematics Research Notices, to appear, arXiv:2509.09098
  2. Diameter, area, and mean curvature, with J. Marx-Kuo
    Differential Geometry and its Applications 103 (2026), Article 102376, DOI 10.1016/j.difgeo.2026.102376, arXiv:2412.04636
  3. On the relative isoperimetric problem for the cube, with L. Mouillé
    Indiana University Mathematics Journal, to appear, arXiv:2302.04382
  4. A note on Kalai's 3d Conjecture, with E. Portnoy
    Electronic Journal of Combinatorics 33(3) (2026), Paper P3.24, DOI 10.37236/13956, arXiv:2211.09215
  5. On minimal higher genus fillings
    Journal of Topology and Analysis, published online April 9, 2026, pp. 1–15, DOI 10.1142/S1793525326500184, arXiv:2202.01342
  6. A note on the affine-invariant plank problem, with L. Mouillé
    Rocky Mountain Journal of Mathematics, to appear, arXiv:1604.00456
  7. On the square peg problem
    Discrete & Computational Geometry 73(4) (2025), 1144–1153, DOI 10.1007/s00454-025-00720-x, arXiv:2203.02613
  8. Geodesic nets on non-compact Riemannian manifolds, with Y. Liokumovich, A. Nabutovsky, and R. Rotman
    Journal for pure and applied mathematics (Crelles Journal), vol. 2023, no. 799, 2023, pp. 287-303, DOI 10.1515/crelle-2023-0028
  9. A stability result for Riesz potentials in higher dimensions, with A. Burchard
    Indiana University Mathematics Journal, to appear, arXiv:2007.11664
  10. The length of the receiver operating characteristic curve and the two cutoff Youden index within a robust framework for discovery, evaluation, and cutoff estimation in biomarker studies involving improper receiver operating characteristic curves, with L. E. Bantis, J. V. Tsimikas, M. Capello, S. M. Hanash, and Z. Feng
    Statistics in Medicine 40(7) (2021), 1767–1789, DOI 10.1002/sim.8869
  11. Constructing monotone homotopies and sweepouts, with E. W. Chambers, A. de Mesmay, T. Ophelders, and R. Rotman
    J. Differential Geom. 119(3): 383-401 (November 2021) DOI 10.4310/jdg/1635368350
  12. Existence of minimal hypersurfaces in complete manifolds of finite volume, with Y. Liokumovich
    Inventiones Mathematicae 219(2020), 179 -- 217 DOI 10.1007/s00222-019-00903-3
  13. Quantitative null-cobordism, with D. Dotterrer, F. Manin, and S. Weinberger
    Journal of the AMS 31(2018), 1165--1203, DOI 10.1090/jams/903
  14. Quantitative nullhomotopy and rational homotopy type, with F. Manin, and S. Weinberger
    Geometric and Functional Analysis 28(2018), 563--588 DOI 10.1007/s00039-018-0450-2
  15. Area of convex disks, with C. Croke, Y. Liokumovich, and H. Wen
    Proceedings of the American Mathematical Society, advance online publication, January 31, 2018, DOI 10.1090/proc/14092, arXiv:1701.06594
  16. Monotone homotopies and contracting discs on Riemannian surfaces, with R. Rotman
    Journal of Topology and Analysis 10(2018) 323--354, DOI 10.1142/S1793525318500103
  17. Optimal sweepouts of a Riemannian 2-sphere, with Y. Liokumovich
    Journal of the European Mathematics Society 21(5):1361-1377 (2019), DOI 10.4171/JEMS/863
  18. Proof of the Log-Convex Density Conjecture
    Journal of the European Mathematics Society 21(8):2301-2332 (2019), DOI 10.4171/JEMS/885
  19. Ergodic properties of folding maps on spheres, with A. Burchard and A. Dranovski
    Discrete and Continuous Dynamical Systems - Series A 37(3):1183-1200 (2017), DOI 10.3934/dcds.2017049
  20. Isoperimetric regions in \(\mathbb{R}^n\) with density \(r^p\), with W. Boyer, B. Brown, A. Loving, and S. Tammen
    Analysis and Geometry in Metric Spaces 4(1):236-265 (2016), DOI 10.1515/agms-2016-0009
  21. Splitting a contraction of a simple curve traversed \(m\) times, with Y. Liokumovich
    Journal of Topology and Analysis 9(2016) 409--418, DOI 10.1142/S1793525317500157
  22. Geometric stability of the Coulomb energy, with A. Burchard
    Calculus of Variations and PDE 54(3):3241-3250 (2015), DOI 10.1007/s00526-015-0900-8
  23. Perimeter under multiple Steiner symmetrizations, with A. Burchard
    Journal of Geometric Analysis (2015) 25:871, DOI 10.1007/s12220-013-9448-z
  24. Converting homotopies to isotopies and dividing homotopies in half in an effective way, with Y. Liokumovich
    Geometric and Functional Analysis (2014) 24:1080, DOI 10.1007/s00039-014-0283-6