77 citations · 178 across the 21 of their papers we have counts for
21 papers
A metric on with positive sectional curvature
S. Brendle, P. K. Hung
We construct a metric on with positive sectional curvature. Starting from the standard metric on , we first perform a Cheeger deformation. The resu…
Geometric inequalities and the Alexandrov-Bakelman-Pucci technique
S. Brendle
In this expository paper, we discuss a unified framework for proving various geometric inequalities, based on the so-called Alexandrov-Bakelman-Pucci technique. Examples include Ca…
Systolic inequalities and the Horowitz-Myers conjecture
S. Brendle, P. K. Hung
Let be an integer with , let be a compact manifold of dimension with boundary , and let be a Riemannian metric on with scalar curva…
Minimal hypersurfaces and geometric inequalities
S. Brendle
In this expository paper, we discuss some of the main geometric inequalities for minimal hypersurfaces. These include the classical monotonicity formula, the Alexander-Osserman con…
A monotonicity formula for mean curvature flow with surgery
S. Brendle
We prove a monotonicity formula for mean curvature flow with surgery. This formula differs from Huisken's monotonicity formula by an extra term involving the mean curvature. As a c…
An inscribed radius estimate for mean curvature flow in Riemannian manifolds
S. Brendle
We consider a family of embedded, mean convex hypersurfaces in a Riemannian manifold which evolve by the mean curvature flow. We show that, given any number and any , we…