126 citations · 500 across the 19 of their papers we have counts for
25 papers
On the first and second homotopy groups of manifolds with positive curvature
Richard Schoen
We show that an odd dimensional closed manifold with positive curvature cannot contain an incompressible real projective plane in the sense that there is no map of the projective p…
Stability and largeness properties of minimal surfaces in higher codimension
Ailana Fraser, Richard Schoen
We consider stable minimal surfaces of genus 1 in Euclidean space and in Riemannian manifolds. Under the condition of covering stability (all finite covers are stable) we show that…
Some results on higher eigenvalue optimization
Ailana Fraser, Richard Schoen
In this paper we obtain several results concerning the optimization of higher Steklov eigenvalues both in two and higher dimensional cases. We first show that the normalized (by bo…
Shape optimization for the Steklov problem in higher dimensions
Ailana Fraser, Richard Schoen
We show that the ball does not maximize the first nonzero Steklov eigenvalue among all contractible domains of fixed boundary volume in when . This is in c…
Positive Scalar Curvature and Minimal Hypersurface Singularities
Richard Schoen, Shing-Tung Yau
In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass the…
Complete manifolds with bounded curvature and spectral gaps
Richard Schoen, Hung Tran
We study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius. We give general conditions which imply that their essential spectrum…