22 citations · 137 across the 27 of their papers we have counts for
29 papers
(Semi-)Models for Slice Regular Functions on Real Division Algebras
Amedeo Altavilla, Cinzia Bisi
We study slice regular functions on the real division algebras and from the point of view of equivalence under automorphism and conjugation actions. Motiv…
Complex Quaternions and Superminimal Surfaces in Four-Space
Amedeo Altavilla, Elena Giorgio
We develop a quaternionic approach to conformal superminimal surfaces in Euclidean four-space. The starting point is the classical Weierstrass representation: every conformal minim…
The Flat CR Twistor Model and Its Algebraic Sections
Amedeo Altavilla, Stefano Marini
We study the flat CR twistor model by explicit projective methods. Using the anti-holomorphic involution associated with the twistor fibration, w…
Geometry of the Donaldson-Friedman Pushout: Twistor degenerations and instanton charge
Amedeo Altavilla, Maurício Corrêa
We study the Donaldson-Friedman semistable twistor degeneration by combining the scheme-theoretic geometry of its Ferrand pushout with the logarithmic topology of its Kato-Nakayama…
Jordan-Segmentable Masks: A Topology-Aware definition for characterizing Binary Image Segmentation
Serena Grazia De Benedictis, Amedeo Altavilla, Nicoletta Del Buono
Image segmentation plays a central role in computer vision. However, widely used evaluation metrics, whether pixel-wise, region-based, or boundary-focused, often struggle to captur…
A Complete Characterization of Pythagorean Hodograph Preserving Mappings
Amedeo Altavilla, Hans-Peter Schröcker, Zbyněk Šír +1
We fully characterize the mappings that send every Pythagorean-hodograph (PH) curve to a PH curve. We prove that in any dimension, such mappings are precisely the conformal fun…
-Fock Space of -Analytic Functions and its realization in
Amedeo Altavilla, Swanhild Bernstein, Martha Lina Zimmermann
We introduce a -deformation of the Fock space of holomorphic functions on , based on a geometric definition of -analyticity. This definition is inspired by a stan…
Minimal Surfaces via Complex Quaternions
Amedeo Altavilla, Hans-Peter Schröcker, Zbyněk Šír +1
Minimal surfaces play a fundamental role in differential geometry, with applications spanning physics, material science, and geometric design. In this paper, we explore a novel qua…
Conjugate -harmonic Polynomials in -Clifford Analysis
Swanhild Bernstein, Amedeo Altavilla, Martha Lina Zimmermann
We consider the problem of constructing a conjugate -harmonic homogeneous polynomial of degree to a given -harmonic homogeneous polynomial of de…
The -exponential as a covering map
Amedeo Altavilla, Samuele Mongodi
We employ tools from complex analysis to construct the -logarithm of a quaternionic slice regular function. Our approach enables us to achieve three main objectives: we compute…
Twistor fibers in hypersurfaces of the flag threefold
Amedeo Altavilla, Edoardo Ballico, Maria Chiara Brambilla
We study surfaces of bidegree (1,d) contained in the flag threefold in relation to the twistor projection. In particular, we focus on the number and the arrangement of twistor fibe…
Surfaces in the flag threefold containing smooth conics and twistor fibers
Amedeo Altavilla, Edoardo Ballico, Maria Chiara Brambilla
We study smooth integral curves of bidegree , called \textit{smooth conics}, in the flag threefold . The study is motivated by the fact that the family of smooth…
Twistor geometry of the Flag manifold
Amedeo Altavilla, Edoardo Ballico, Maria Chiara Brambilla +1
A study is made of algebraic curves and surfaces in the flag manifold , and their configuration relative to the twistor projection from to th…
Slice regular functions as covering maps and global -roots
Amedeo Altavilla, Samuele Mongodi
The aim of this paper is to prove that a large class of quaternionic slice regular functions result to be (ramified) covering maps. By means of the topological implications of this…
-Logarithm for Slice Regular Functions
Amedeo Altavilla, Chiara de Fabritiis
In this paper, we study the (possible) solutions of the equation , where is a slice regular never vanishing function on a circular domain of the quaternions $\ma…
Spherical coefficients of slice regular functions
Amedeo Altavilla
Given a quaternionic slice regular function , we give a direct and effective way to compute the coefficients of its spherical expansion at any point. Such coefficients are obtai…
Canonical models on strongly convex domains via the squeezing function
Amedeo Altavilla, Leandro Arosio, Lorenzo Guerini
We prove that if a holomorphic self-map of a bounded strongly convex domain with smooth boundary is hyperbolic then it admits a natural semi…
Equivalence of slice semi-regular functions via Sylvester operators
Amedeo Altavilla, Chiara de Fabritiis
The aim of this paper is to study some features of slice semi-regular functions on a circular domain contained in the skew-symmetric algebra of quaternions $\…
Implementing zonal harmonics with the Fueter principle
Amedeo Altavilla, Hendrik De Bie, Michael Wutzig
By exploiting the Fueter theorem, we give new formulas to compute zonal harmonic functions in any dimension. We first give a representation of them as a result of a suitable ladder…
Algebraic surfaces with infinitely many twistor lines
Amedeo Altavilla, Edoardo Ballico
We prove that a reduced and irreducible algebraic surface in containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quate…
Three Topological Results on the Twistor Discriminant Locus in the 4-Sphere
Amedeo Altavilla, Edoardo Ballico
We exploit techniques from classical (real and complex) algebraic geometry for the study of the standard twistor fibration . We prove three results abou…
-exponential of slice-regular functions
Amedeo Altavilla, Chiara de Fabritiis
According to [5] we define the -exponential of a slice-regular function, which can be seen as a generalization of the complex exponential to quaternions. Explicit formulas for $…
Twistor lines on algebraic surfaces
Amedeo Altavilla, Edoardo Ballico
We give quantitative and qualitative results on the family of surfaces in containing finitely many twistor lines. We start by analyzing the ideal sheaf of a finite…
S-regular functions which preserve a complex slice
Amedeo Altavilla, Chiara de Fabritiis
We study global properties of quaternionic slice regular functions (also called s-regular) defined on symmetric slice domains. In particular, thanks to new techniques and points of…