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math.DG2025
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…
math.CV2025
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…