4 citations · 7 across the 11 of their papers we have counts for
14 papers
A table of genus two handlebody-knots with seven crossings
Giovanni Bellettini, Giovanni Paolini, Maurizio Paolini +1
We enumerate all genus two handlebody-knots with seven crossings, up to mirror image, extending the Ishii-Kishimoto-Moriuchi-Suzuki table.
Handlebody-knots obtained by tangle replacement
Giovanni Bellettini, Giovanni Paolini, Maurizio Paolini +1
We study tangle replacement in the context of handlebody-knots. The main results classify the handlebody-knots obtained by performing tangle replacement on the prime spatial handcu…
On unique decomposition of knotted handlebodies
Giovanni Bellettini, Maurizio Paolini, Yi-Sheng Wang
The paper considers the uniqueness question of factorization of a knotted handlebody in the -sphere along decomposing -spheres. We obtain a uniqueness result for factorizatio…
A free boundary singular transport equation as a formal limit of a discrete dynamical system
Giovanni Bellettini, Alessandro Betti, Maurizio Paolini
We study the continuous version of a hyperbolic rescaling of a discrete game, called open mancala. The resulting PDE turns out to be a singular transport equation, with a forcing t…
A table of -component handlebody links of genus up to six crossings
Giovanni Bellettini, Giovanni Paolini, Maurizio Paolini +1
A handlebody link is a union of handlebodies of positive genus embedded in 3-space, which generalizes the notion of links in classical knot theory. In this paper, we consider handl…
Numerical irreducibility criteria for handlebody links
Giovanni Bellettini, Maurizio Paolini, Yi-Sheng Wang
In this paper we define a set of numerical criteria for a handlebody link to be irreducible. It provides an effective, easy-to-implement method to determine the irreducibility of h…
A complete invariant for closed surfaces in the three-sphere
Giovanni Bellettini, Maurizio Paolini, Yi-Sheng Wang
Associated to an embedded surface in the -sphere, we construct a diagram of fundamental groups, and prove that it is a complete invariant, wherefrom we deduce complete invariant…
On closed oriented surfaces in the 3-sphere
Giovanni Bellettini, Maurizio Paolini, Yi-Sheng Wang
In this paper we study embeddings of oriented connected closed surfaces in . We define a complete invariant, the fundamental span, for such embeddings, generalizing th…
On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions
Giovanni Bellettini, Alaa Elshorbagy, Maurizio Paolini +1
In this paper we estimate from above the area of the graph of a singular map taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2-…
Covers, soap films and BV functions
Giovanni Bellettini, Maurizio Paolini, Franco Pasquarelli +1
In this paper we first review the covering space method with constrained BV functions for solving the classical Plateau's problem. Next, we carefully analyze some interesting examp…
Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone
Giovanni Bellettini, Maurizio Paolini, Franco Pasquarelli
By using a suitable triple cover we show how to possibly model the construction of a minimal surface with positive genus spanning all six edges of a tetrahedron, working in the spa…
Exploring the "Rubik's Magic" universe
Maurizio Paolini
By using two different invariants for the Rubik's Magic puzzle, one of metric type, the other of topological type, we can dramatically reduce the universe of constructible configur…
On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity
Giovanni Bellettini, Maurizio Paolini, Lucia Tealdi
In this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discont…
An optimal bound on the number of moves for open Mancala
Alessandro Musesti, Maurizio Paolini, Cesco Reale
We determine the optimal bound for the maximum number of moves required to reach a periodic configuration of open mancala (also called open owari), inspired by a popular African ga…