Robin Neumayer Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, IL 60208 Office: Lunt Hall 301 E-Mail: neumayer [at] math [dot] northwestern [dot] edu

I am an RTG Postdoctoral Fellow at Northwestern University. My research is partly supported by NSF Grant DMS-1901427 "Stability of functional and geometric inequalities and applications'' (2019-2022).

I was a member of the Institute for Advanced Study for the 2018-19 academic year, participating in the special year on Variational Methods in Geometry there. I completed my Ph.D. at UT Austin under the supervision of Alessio Figalli and Francesco Maggi. I work in the calculus of variations, PDE, and geometric analysis.

You can find my CV here (last updated July 2021).

Publications and Preprints

• Sharp quantitative Faber-Krahn inequalities and the Alt-Caffarelli-Friedman monotonicity formula (.pdf)
  with M. Allen and D. Kriventsov.
  Submitted paper.


• Linear Stability Implies Nonlinear Stability for Faber-Krahn Type Inequalities (.pdf)
  with M. Allen and D. Kriventsov.
  Submitted paper.


• \(d_p\) Convergence and \(\epsilon\)-regularity theorems for scalar curvature and entropy lower bounds (.pdf)
  with M.-C. Lee and A. Naber.
  Submitted paper.


• Quantitative stability for minimizing Yamabe metrics (.pdf)
  with M. Engelstein and L. Spolaor.
  Submitted paper.


• 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.
  Accepted to Adv. Calc. Var.


• 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

• Convergence and regularity of manifolds with scalar curvature and entropy lower bounds. (.pdf)
  to appear in Perspectives in Scalar Curvature.


• Characterizing minimizers of a constrained planar isoperimetric problem. (.pdf)
  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