Robin Neumayer Associate Professor Department of Mathematical Sciences Carnegie Mellon University Wean Hall 7121 neumayer [at] cmu [dot] edu

I am an associate professor in the Department of Mathematical Sciences at Carnegie Mellon University. My research lies at the interface of the calculus of variations, PDE, and geometric analysis. My work is partly supported by NSF CAREER: Geometric aspects of isoperimetric and Sobolev-type inequalities (DMS-2340195, 2024-2029) and I am a co-PI on our group's NSF RTG: Frontiers in Applied Analysis (DMS-2342349, 2024-2029).

Before joining the faculty at CMU, I was an RTG Postdoctoral Fellow at Northwestern University for the 2017-18 and 2019-21 academic years, and I spent the 2018-19 academic year as a member at the Institute for Advanced Study participating in the Variational Methods in Geometry special year. I completed my Ph.D. at UT Austin under the supervision of Alessio Figalli and Francesco Maggi.

You can find my CV here (last updated Aug. 2025).

Publications and Preprints

• Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane. (.pdf)
  with E. Mäder-Baumdicker, J. Park, and M. Rupflin.
  Preprint.


• On the non-uniqueness of locally minimizing clusters via singular cones. (.pdf)
  with L. Bronsard, M. Novack, and A. Skorobogatova.
  Preprint.


• Quantitative Resolvent and Eigenfunction Stability for the Faber-Krahn Inequality. (.pdf)
  with M. Allen and D. Kriventsov.
  Preprint.


• Local minimizers of the anisotropic isoperimetric problem on closed manifolds. (.pdf)
  with A. De Rosa.
  Indiana U. Math. J (2024).


• Epsilon regularity under scalar curvature and entropy lower bounds and volume upper bounds. (.pdf)
  CMSA Special Year Program on General Relativity and Scalar Curvature, Harvard CMSA book series, vol. 4. 2024.


• Rectifiability and uniqueness of blow-ups for points with positive Alt-Caffarelli-Friedman limit. (.pdf)
  with M. Allen and D. Kriventsov.
  Math. Ann. 391 (2025), no. 4, 6251-6289.


• Rigidity theorems for best Sobolev inequalities. (.pdf)
  with F. Maggi and I. Tomasetti.
  Adv. Math. 434 (2023) 109330.


• Sharp quantitative Faber-Krahn inequalities and the Alt-Caffarelli-Friedman monotonicity formula (.pdf)
  with M. Allen and D. Kriventsov.
  Ars Inven. Anal. 2023, Paper No. 1, 49 pp.


• Linear Stability Implies Nonlinear Stability for Faber-Krahn Type Inequalities (.pdf)
  with M. Allen and D. Kriventsov.
  Interfaces Free Bound. 25(2):217–324, 2023.


• \(d_p\) Convergence and \(\epsilon\)-regularity theorems for scalar curvature and entropy lower bounds (.pdf)
  with M.-C. Lee and A. Naber.
  Geom. Topol. 27-1 (2023), 227–350.


• Quantitative stability for minimizing Yamabe metrics (.pdf)
  with M. Engelstein and L. Spolaor.
  Trans. Amer. Math. Soc. Ser. B., 9 (2022), 395–414.


• A note on strong-form stability for the Sobolev inequality (.pdf)
  Calc. Var. Partial Differential Equations, 59 (2020), no. 1, Paper No. 25, 8pp.


• Anisotropic liquid drop models (.pdf )
  with R. Choksi and I. Topaloglu.
  Adv. Calc. Var., 15 (2022) no. 1, 109-131


• Bubbling with \(L^2\)-almost constant mean curvature and an Alexandrov-type theorem for crystals (.pdf)
  with M.G. Delgadino, F. Maggi, and C. Mihaila.
  Arch. Ration. Mech. Anal. 230 (2018) no. 3, 1131–1177.
  


• The Cheeger constant of a Jordan domain without necks (.pdf)
  with G.P. Leonardi and G. Saracco.
  Calc. Var. Partial Differential Equations. 56 (2017), no. 6, 56:164.


• A bridge between Sobolev and Escobar inequalities and beyond (.pdf)
  with F. Maggi.
  J. Funct. Anal. 273 (2017), no. 6, 2070–2106.


• Higher regularity of the free boundary in the obstacle problem for the fractional Laplacian (.pdf)
  with Y. Jhaveri.
  Adv. Math. 311 (2017), 748–795.


• Gradient stability for the Sobolev inequality: the case \(p\geq 2\) (.pdf)
  with A. Figalli.
  J. Eur. Math. Soc. (JEMS). 21 (2019), no. 2, 319–354.


• A strong form of the quantitative Wulff inequality (.pdf)
  SIAM J. Math. Anal. 48 (2016), no. 3, 1727–1772.


• A note on the stability of the Cheeger constant of N-gons (.pdf )
  with M. Caroccia.
  J. Convex Anal. 22 (2015), no. 4, 1207–1213.

Proceedings and Surveys

• Existence of Extremals and Rigidity for Optimal Sobolev Inequalities. (.pdf)
  Geometrie. Oberwolfach Rep.. 19 (2022), no. 2, pp. 1551–1601.


• Convergence and regularity of manifolds with scalar curvature and entropy lower bounds. (.pdf)
  Perspectives in Scalar Curvature. Vol. 1, pages 543–576. World. Sci. Publ., Hackensack, NJ, 2023.


• Characterizing minimizers of a constrained planar isoperimetric problem. (.pdf)
  PDE Oberwolfach Rep. 16 (2019), no. 3, 2046–2048.


• On minimizers and critical points for anisotropic isoperimetric problems (.pdf)
  2018 Matrix Annals, 293–302.


• Mass transportation methods in functional inequalities and a new family of sharp constrained Sobolev inequalities (.pdf)
  RIMS Kôkyûroku (2017), no. 2046, 39–49.

Ph.D. Thesis

• Stability and minimality properties in Sobolev and isoperimetric inequalities (.pdf)
  (2017).

Expository Notes

• The Yamabe problem (.pdf)
  

Teaching