## 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 Dec. 2020).

### Publications and Preprints

• $$d_p$$ 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 Reports

• Characterizing minimizers of a constrained planar isoperimetric problem. (.pdf)
to appear in Oberwolfach Reports.

• On minimizers and critical points for anisotropic isoperimetric problems (.pdf)
to appear in 2018 Matrix Annals.

• 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

I am teaching Introduction to Differential Geometry (Math 342) for the Fall 2020 quarter. Please consult Canvas for information about the course.