Robin Neumayer

activity

20142026

L^{2}

-almost constant mean curvature and an Alexandrov-type theorem for crystals

33 citations · 61 across the 17 of their papers we have counts for

collaborators

23 papers

math.AP2026

Minimizing clusters with prescribed asymptotic geometry

Robin Neumayer, Michael Novack, Anna Skorobogatova

We construct locally minimizing $(1, 2)$ -clusters whose exterior interfaces are asymptotic to various prescribed singular area-minimizing cones. For $n + 1 \leq 7$ , Bronsard & Novack…

math.AP2026

Qualitative stability for a family of trace Sobolev inequalities

Robin Neumayer

The goal of this short note is to prove qualitative stability for a family of trace Sobolev inequalities first proven by Carlen \& Loss for $p = 2$ and by Maggi and the author for $p…

math.AP2025

Rigidity of critical points of hydrophobic capillary functionals

Antonio De Rosa, Robin Neumayer, Reinaldo Resende

We prove the rigidity, among sets of finite perimeter, of volume-preserving critical points of the capillary energy in the half space, in the case where the prescribed interior con…

math.AP2025

Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane

Elena Mäder-Baumdicker, Robin Neumayer, Jiewon Park +1

We prove three related quantitative results for the relative isoperimetric problem outside a convex body $Ω$ in the plane: (1) Łojasiewicz estimates and quantitative rigidity for c…

math.AP2025

On the non-uniqueness of locally minimizing clusters via singular cones

Lia Bronsard, Robin Neumayer, Michael Novack +1

We construct partitions of $R^{n}$ into three sets ${X (1), X (2), X (3)}$ that locally minimize interfacial area among compactly supported volume…

math.AP2025

Quantitative Resolvent and Eigenfunction Stability for the Faber-Krahn Inequality

Mark Allen, Dennis Kriventsov, Robin Neumayer

For a bounded open set $Ω \subset R^{n}$ with the same volume as the unit ball, the classical Faber-Krahn inequality says that the first Dirichlet eigenvalue $λ_{1} (Ω)$ of the…

math.AP2023

Local Minimizers of the Anisotropic Isoperimetric Problem on Closed Manifolds

Antonio De Rosa, Robin Neumayer

Local minimizers for the anisotropic isoperimetric problem in the small-volume regime on closed Riemannian manifolds are shown to be geodesically convex and small smooth perturbati…

math.DG2022

Epsilon regularity under scalar curvature and entropy lower bounds and volume upper bounds

Robin Neumayer

Examples show that Riemannian manifolds with almost-Euclidean lower bounds on scalar curvature and Perelman entropy need not be close to Euclidean space in any metric space sense.…

math.AP2022★ 1 cited

Rectifiability and uniqueness of blow-ups for points with positive Alt-Caffarelli-Friedman limit

Mark Allen, Dennis Kriventsov, Robin Neumayer

We study the regularity of the interface between the disjoint supports of a pair of nonnegative subharmonic functions. The portion of the interface where the Alt-Caffarelli-Friedma…

math.AP2022

Rigidity theorems for best Sobolev inequalities

Francesco Maggi, Robin Neumayer, Ignacio Tomasetti

For $n \geq 2$ , $p \in (1, n)$ , the "best $p$ -Sobolev inequality" on an open set $Ω \subset R^{n}$ is identified with a family $Φ_{Ω}$ of variational problems with critical volume a…

math.AP2021★ 1 cited

Sharp quantitative Faber-Krahn inequalities and the Alt-Caffarelli-Friedman monotonicity formula

Mark Allen, Dennis Kriventsov, Robin Neumayer

The objective of this paper is two-fold. First, we establish new sharp quantitative estimates for Faber-Krahn inequalities on simply connected space forms. We prove that the gap be…

math.AP2021

Linear Stability Implies Nonlinear Stability for Faber-Krahn Type Inequalities

Mark Allen, Dennis Kriventsov, Robin Neumayer

For a domain $Ω \subset R^{n}$ and a small number $T > 0$ , let \[ \mathcal{E}_0(Ω) = λ_1(Ω) + {\frak{T}} {\text{tor}}(Ω) = \inf_{u, w \in H^1_0(Ω)\setminus \{0\}} \fra…

math.DG2020★ 4 cited

$d_{p}$ convergence and $ε$ -regularity theorems for entropy and scalar curvature lower bounds

Man-Chun Lee, Aaron Naber, Robin Neumayer

Consider a sequence of Riemannian manifolds $(M_{i}^{n}, g_{i})$ with scalar curvatures and entropies bounded below by small constants $R_{i}, μ_{i} \geq - ε_{i}$ . The goal of this paper is to und…

math.AP2020

Quantitative Stability for Minimizing Yamabe Metrics

Max Engelstein, Robin Neumayer, Luca Spolaor

On any closed Riemannian manifold of dimension $n \geq 3$ , we prove that if a function nearly minimizes the Yamabe energy, then the corresponding conformal metric is close, in a qua…

math.AP2019

A note on strong-form stability for the Sobolev inequality

Robin Neumayer

In this note, we establish a strong form of the quantitive Sobolev inequality in Euclidean space for $p \in (1, n)$ . Given any function $u \in W ˙^{1, p} (R^{n})$ , the gap i…

math.AP2018

Anisotropic liquid drop models

Rustum Choksi, Robin Neumayer, Ihsan Topaloglu

We introduce and study certain variants of Gamow's liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are est…

math.AP2017★ 33 cited

Bubbling with $L^{2}$ -almost constant mean curvature and an Alexandrov-type theorem for crystals

M. G. Delgadino, F. Maggi, C. Mihaila +1

A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measu…

math.AP2017★ 21 cited

The Cheeger constant of a Jordan domain without necks

Gian Paolo Leonardi, Robin Neumayer, Giorgio Saracco

We show that the maximal Cheeger set of a Jordan domain $Ω$ without necks is the union of all balls of radius $r = h (Ω)^{- 1}$ contained in $Ω$ . Here, $h (Ω)$ denotes the Cheeger con…

math.AP2016

A bridge between Sobolev and Escobar inequalities and beyond

Francesco Maggi, Robin Neumayer

The classical Sobolev and Escobar inequalities are embedded into the same one-parameter family of sharp trace-Sobolev inequalities on half-spaces. Equality cases are characterized…

math.AP2016

Higher Regularity of the Free Boundary in the Obstacle Problem for the Fractional Laplacian

Yash Jhaveri, Robin Neumayer

We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack inequality.

math.AP2015

Gradient stability for the Sobolev inequality: the case $p \geq 2$

Alessio Figalli, Robin Neumayer

We prove a strong form of the quantitative Sobolev inequality in $R^{n}$ for $p \geq 2$ , where the deficit of a function $u \in W ˙^{1, p}$ controls $\| \nabla u -\nabla v\…

math.AP2015

A strong form of the quantitative Wulff inequality

Robin Neumayer

Quantitative isoperimetric inequalities for anisotropic surface energies are shown where the isoperimetric deficit controls both the Fraenkel asymmetry and a measure of the oscilla…

math.AP2014★ 1 cited

A note on the stability of the Cheeger constant of $N$ -gons

Marco Caroccia, Robin Neumayer

The regular $N$ -gon provides the minimal Cheeger constant in the class of all $N$ -gons with fixed volume. This result is due to a work of Bucur and Fragalà in 2014. In this note, w…

Minimizing clusters with prescribed asymptotic geometry

Qualitative stability for a family of trace Sobolev inequalities

Rigidity of critical points of hydrophobic capillary functionals

Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane

On the non-uniqueness of locally minimizing clusters via singular cones

Quantitative Resolvent and Eigenfunction Stability for the Faber-Krahn Inequality

Local Minimizers of the Anisotropic Isoperimetric Problem on Closed Manifolds

Epsilon regularity under scalar curvature and entropy lower bounds and volume upper bounds

Rectifiability and uniqueness of blow-ups for points with positive Alt-Caffarelli-Friedman limit

Rigidity theorems for best Sobolev inequalities

Sharp quantitative Faber-Krahn inequalities and the Alt-Caffarelli-Friedman monotonicity formula

Linear Stability Implies Nonlinear Stability for Faber-Krahn Type Inequalities

dp​ convergence and ε-regularity theorems for entropy and scalar curvature lower bounds

Quantitative Stability for Minimizing Yamabe Metrics

A note on strong-form stability for the Sobolev inequality

Anisotropic liquid drop models

Bubbling with L2-almost constant mean curvature and an Alexandrov-type theorem for crystals

The Cheeger constant of a Jordan domain without necks

A bridge between Sobolev and Escobar inequalities and beyond

Higher Regularity of the Free Boundary in the Obstacle Problem for the Fractional Laplacian

Gradient stability for the Sobolev inequality: the case p≥2

A strong form of the quantitative Wulff inequality

A note on the stability of the Cheeger constant of N-gons

$d_{p}$ convergence and $ε$ -regularity theorems for entropy and scalar curvature lower bounds

Bubbling with $L^{2}$ -almost constant mean curvature and an Alexandrov-type theorem for crystals

Gradient stability for the Sobolev inequality: the case $p \geq 2$

A note on the stability of the Cheeger constant of $N$ -gons