21 citations · 43 across the 7 of their papers we have counts for
8 papers
Sobolev-Trace inequalities of order four
Antonio Ache, Sun-Yung Alice Chang
We establish sharp Sobolev inequalities of order four on Euclidean d-balls for d greater than or equal to four. When d=4, our inequality generalizes the classical second order Lebe…
Coarse Ricci curvature as a function on
Antonio Ache, Micah Warren
We use the framework used by Bakry and Emery in their work on logarithmic Sobolev inequalities to define a notion of coarse Ricci curvature on smooth metric measure spaces alternat…
Metrics with non-negative Ricci curvature on convex three-manifolds
Antonio Ache, Davi Maximo, Haotian Wu
We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path connected; and, moreover, that the ass…
Approximating coarse Ricci curvature on submanifolds of Euclidean space
Antonio Ache, Micah Warren
For an embedded submanifold , Belkin and Niyogi showed that one can approximate the Laplacian operator using heat kernels. Using a definition of coarse Ricc…
Ricci Curvature and the Manifold Learning Problem
Antonio G. Ache, Micah W. Warren
Consider a sample of points taken i.i.d from a submanifold of Euclidean space. We show that there is a way to estimate the Ricci curvature of with respect to the induce…
On the uniqueness of asymptotic limits of the Ricci flow
Antonio G. Ache
We consider a normalization of the Ricci flow on a closed Riemannian manifold given by the evolution equation where is a fixed…
Asymptotics of the self-dual deformation complex
Antonio G. Ache, Jeff A. Viaclovsky
We analyze the indicial roots of the self-dual deformation complex on a cylinder , where is a space of constant curvature. An application…
Obstruction-flat asymptotically locally Euclidean metrics
Antonio Ache, Jeff Viaclovsky
We show that any asymptotically locally Euclidean (ALE) metric which is obstruction-flat or extended obstruction-flat must be ALE of a certain optimal order. Moreover, our proof ap…