8 papers
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…
A Complete Characterization of Pythagorean Hodograph Preserving Mappings
Amedeo Altavilla, Hans-Peter Schröcker, ZbynÄk Å Ãr +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 fu…
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, MaurÃcio Corrêa
We study the singular central fibre arising in the Donaldson-Friedman construction for twistor spaces of connected sums, viewing it as a Ferrand pushout of two blown-up twistor spa…
Minimal Surfaces via Complex Quaternions
Amedeo Altavilla, Hans-Peter Schröcker, ZbynÄk Å Ãr +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…
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…