4 citations · 13 across the 14 of their papers we have counts for
15 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…
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…
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…
A general nonuniqueness result for Yamabe-type problems for conformally variational Riemannian invariants
João Henrique Andrade, Jeffrey S. Case, Paolo Piccione +1
Given a conformally variational scalar Riemannian invariant , we identify a sufficient condition for a compact Riemannian manifold to admit finite regular coverings with many no…
Complete metrics with constant fractional higher order -curvature on the punctured sphere
João Henrique Andrade, Juncheng Wei, Zikai Ye
This manuscript is devoted to constructing complete metrics with constant higher fractional curvature on punctured spheres with finitely many isolated singularities. Analytically,…
Nonuniqueness results for constant sixth order -curvature metrics on spheres with higher dimensional singularities
João Henrique Andrade, Paolo Piccione, Juncheng Wei
We prove nonuniqueness results for constant sixth order -metrics on complete locally conformally flat -dimensional Riemannian manifolds with . More precisely, a…
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…
Asymptotics for positive singular solutions to subcritical sixth order equations
João Henrique Andrade, Juncheng Wei
We classify the local asymptotic behavior of positive singular solutions to a class of subcritical sixth order equations on the punctured ball. Initially, using a version of the in…
Classification for positive singular solutions to critical sixth order equations
João Henrique Andrade, Juncheng Wei
We classify entire positive singular solutions to a family of critical sixth order equations in the punctured space with a non-removable singularity at the origin. More precisely,…
Multiplicity of solutions to the multiphasic Allen-Cahn-Hilliard system with a small volume constraint on closed parallelizable manifolds
João Henrique Andrade, Jackeline Conrado, Stefano Nardulli +2
We prove the existence of multiple solutions to the Allen--Cahn--Hilliard (ACH) vectorial equation (with two equations) involving a triple-well (triphasic) potential with a small v…
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…
Qualitative properties for solutions to subcritical fourth order systems
João Henrique Andrade, João Marcos do Ó
We prove some qualitative properties for singular solutions to a class of strongly coupled system involving a Gross--Pitaevskii-type nonlinearity. Our main theorems are vectorial f…
Asymptotics for singular solutions to conformally invariant fourth order systems in the punctured ball
João Henrique Andrade, João Marcos do Ó
We study the asymptotic behavior for singular solutions to a critical fourth order system generalizing the constant -curvature equation. Our main result extends to the case of s…
Qualitative properties for solutions to conformally invariant fourth order critical systems
João Henrique Andrade, João Marcos do Ó
We study qualitative properties for nonnegative solutions to a conformally invariant coupled system of fourth order equations involving critical exponents. For solutions defined in…