10 citations · 45 across the 23 of their papers we have counts for
25 papers
Existence of Yamabe stability optimizers
João Henrique Andrade, Tobias König, Jesse Ratzkin +1
We prove the existence of stability optimizers for the Yamabe inequality on closed Riemannian manifolds of dimension at least three with positive Yamabe invariant that satisfy two…
Weighted Hardy-Sobolev type inequalities with boundary terms
João Marcos do Ò, Marcelo Furtado, Everaldo Medeiros +1
In this paper we establish a new class of weighted Hardy-Sobolev type inequalities under mild monotonicity assumptions on the weight function. As a consequence, we derive the corre…
Classification of fractional, singular Yamabe metrics on a twice punctured sphere I
João Henrique Andrade, Azahara DelaTorre, João Marcos do Ò +2
The Delaunay metrics form a family of conformally flat, constant fractional Q-curvature metrics on a twice-punctured sphere. They are all (after a Möbius transformation) rotational…
An end to end gluing construction for metrics of constant Q-curvature
A. Sophie Aiken, Rayssa Caju, Jesse Ratzkin +1
We produce many new complete, constant Q-curvature metrics on finitely punctured spheres by gluing together known examples. In our construction we truncate one end of each summand…
Quantitative stability of the total -curvature near minimizing metrics
João Henrique Andrade, Tobias König, Jesse Ratzkin +1
Under appropriate positivity hypotheses, we prove quantitative estimates for the total -th order -curvature functional near minimizing metrics on any smooth, closed -dimen…
Moduli space theory for complete, constant Q-curvature metrics on finitely punctured spheres
Rayssa Caju, Jesse Ratzkin, Almir Silva Santos
We study constant Q-curvature metrics conformal to the round metric on the sphere with finitely many point singularities. We show that the moduli space of solutions with finitely m…
Compactness of singular solutions to the sixth order GJMS equation
João Henrique Andrade, João Marcos do Ò, Jesse Ratzkin +1
We study compactness properties of the set of conformally flat singular metrics with constant, positive sixth order Q-curvature on a finitely punctured sphere. Based on a recent cl…
Constant Q-curvature metrics with Delaunay ends: the nondegenerate case
João Henrique Andrade, Rayssa Caju, João Marcos do Ó +2
We construct a one-parameter family of solutions to the positive singular Q-curvature problem on compact nondegenerate manifolds of dimension bigger than four with finitely many pu…
Compactness within the space of complete, constant Q-curvature metrics on the sphere with isolated singularities
João Henrique Andrade, João Marcos do Ó, Jesse Ratzkin
In this paper we consider the moduli space of complete, conformally flat metrics on a sphere with k punctures having constant positive Q-curvature and positive scalar curvature. Pr…
Foliation of an asymptotically flat end by critical capacitors
Mouhammed Moustapha Fall, Ignace Aristide Minlend, Jesse Ratzkin
We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. Thes…
On a fourth order conformal invariant
Jesse Ratzkin
In this note we prove that a fourth order conformal invariant on the product of a circle with an (n-1)-dimensional sphere can be arbitrarily close to that of the n-dimensional sphe…
On constant Q-curvature metrics with isolated singularities
Jesse Ratzkin
In this paper we derive a refined asymptotic expansion, near an isolated singularity, for conformally flat metrics with constant positive Q-curvature and positive scalar curvature.…
On the rate of change of the best constant in the Sobolev inequality
Tom Carroll, Mouhamed Moustapha Fall, Jesse Ratzkin
We estimate the rate of change of the best constant in the Sobolev inequality of a Euclidean domain which moves outward. Along the way we prove an inequality which reverses the usu…
Monotonicity of the first Dirichlet eigenvalue of the Laplacian on manifolds of nonpositive curvature
Tom Carroll, Jesse Ratzkin
Let be a complete manifold of nonpositive scalar curvature, let be a suitable domain, and let be the first Dirichlet eigenvalue of the Laplace-Beltrami…
A reverse Holder inequality for extremal Sobolev functions
Tom Carroll, Jesse Ratzkin
Let , let be a bounded domain with smooth boundary, and let . We prove a reverse-Holder inequality for functions realizing th…
A numerical investigation of level sets of extremal Sobolev functions
Stefan Juhnke, Jesse Ratzkin
In this paper we investigate the level sets of extremal Sobolev functions for subcritical exponents p. We conjecture that as p increases the corresponding extremal functions become…
An isoperimetric inequality for extremal Sobolev functions
Tom Carroll, Jesse Ratzkin
Let D be a bounded domain in n-dimensional Euclidean space, where n>2, and let 1<p< (2n)/(n-2). We prove a reverse-Holder inequality for functions realizing equality in the Sobolev…
Two isoperimetric inequalities for the Sobolev constant
Tom Carroll, Jesse Ratzkin
In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation…
Isoperimetric inequalities and variations on Schwarz's lemma
Tom Carroll, Jesse Ratzkin
In this note we prove a version of the classical Schwarz lemma for the first eigenvalues of the Laplacian with Dirichlet boundary data. A key ingredient in our proof is an isoperim…
Interpolating between torsional rigidity and principal frequency
Tom Carroll, Jesse Ratzkin
A one-parameter family of variational problems is introduced that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partia…
Eigenvalues of Euclidean wedge domains in higher dimensions
Jesse Ratzkin
In this paper, we use a weighted isoperimetric inequality to give a lower bound on the first Dirichlet eigenvalue of the Laplacian on a bounded domain inside a Euclidean cone. Our…
A Payne-Weinberger eigenvalue estimate for wedge domains on spheres
Jesse Ratzkin, Andrejs Treibergs
A Faber-Krahn type argument gives a sharp lower estimate for the first Dirichlet eigenvalue for subdomains of wedge domains in spheres, generalizing the inequality in the plane, fo…
Coplanar k-unduloids are nondegenerate
Karsten Grosse-Brauckmann, Nicholas J. Korevaar, Robert B. Kusner +2
We prove each embedded, constant mean curvature (CMC) surface in Euclidean space with genus zero and finitely many coplanar ends is nondegenerate: there is no nontrivial square-int…
A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains
Jesse Ratzkin, Andrejs Treibergs
We resolve a question of Bramson and Griffeath by showing that the expected capture time of four independent Brownian predators pursuing one Brownian prey on a line is finite. Our…