3 papers
math.AP2026
Survey on topological methods for Allen--Cahn equations and systems
João Henrique Andrade, Stefano Nardulli, Raoní Ponciano
We present a survey on multiplicity results for the Allen--Cahn equation and systems in the singular perturbation regime, emphasizing their geometric interpretation through -con…
math.DG2025
Nonhomothetic complete periodic metrics with constant scalar curvature
João H. Andrade, Jeffrey S. Case, Paolo Piccione +1
We show that there are infinitely many pairwise nonhomothetic, complete, periodic metrics with constant scalar curvature that are conformal to the round metric on $S^n\setminus S^k…
math.AP2025
Local asymptotics for singular solutions to critical Hartree equations
João Henrique Andrade, Tao Feng, Paolo Piccione +1
We investigate the qualitative properties of a critical Hartree equation defined on punctured domains. Our study has two main objectives: analyzing the asymptotic behavior near iso…