7 papers
Zoll manifolds with boundary
Eduardo Longa, Paolo Piccione, Roney Santos
We introduce and study Zoll manifolds with boundary: compact Riemannian manifolds with smooth boundary such that every geodesic issuing orthogonally from the boundary returns ortho…
Satellite Links with Multiple Full Twists and Single-Twist Companions
Thiago de Paiva, Yi Liu, Paolo Piccione
We study the relationship between the number of full twists in positive braid representations of satellite links and their companion links. We construct infinitely many satellite l…
Bifurcations of Clifford tori in ellipsoids
Renato G. Bettiol, Paolo Piccione
We prove that 3-dimensional ellipsoids invariant under a 2-torus action contain infinitely many distinct immersed minimal tori, with at most one exception. These minimal tori bifur…
Nonplanar minimal spheres in ellipsoids of revolution
Renato G. Bettiol, Paolo Piccione
We use global bifurcation techniques to establish the existence of arbitrarily many geometrically distinct nonplanar embedded smooth minimal 2-spheres in sufficiently elongated 3-d…
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…
Stable invariant manifold for generalized ODEs with applications to measure differential equations
Weijie Lu, Paolo Piccione, Yonghui Xia
This paper establishes the stable invariant manifold for a new kind of differential equations defined by Kurzweil integral, so-called {\em generalized ODEs} on a Banach space. The…