96 citations · 554 across the 37 of their papers we have counts for
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Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound
Aaron Naber, Daniele Valtorta
We complete the picture of sharp eigenvalue estimates for the p-Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operat…
Critical sets of elliptic equations
Jeff Cheeger, Aaron Naber, Daniele Valtorta
Given a solution to a linear homogeneous second order elliptic equation with Lipschitz coefficients, we introduce techniques for giving improved estimates of the critical set $…
Quantitative Stratification and the Regularity of Mean Curvature Flow
Jeff Cheeger, Robert Haslhofer, Aaron Naber
Let $\cM$ be a Brakke flow of -dimensional surfaces in . The singular set $\cS\subset\cM$ has a stratification $\cS^0\subset\cS^1\subset...\cS$, where $X\in \cS^j$ if no ta…
New logarithmic Sobolev inequalities and an ε-regularity theorem for the Ricci flow
Hans-Joachim Hein, Aaron Naber
In this note we prove a new ε-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) i…