Year: 2026
Type: article
Abstract: Many fractals G admit a harmonic immersion into R n , i.e. an immersion which minimises a natural energy under fixed boundary conditions; we look for harmonic immersions of the Sierpinski gasket into the hyperbolic plane. We show that, given any three points A ~ , B ~ , C ~ in the hyperbolic plane there is a harmonic map bringing the three points A , B , C of the boundary of the gasket to A ~ , B ~ , C ~ respectively. Moreover, if the points A ~ , B ~ , C ~ are sufficiently close in the hyperbolic distance, then the harmonic map is unique and depends differentiably on A ~ , B ~ , C ~ . Lastly, we show that, if the harmonic map φ is injective, then it brings geodesics of the gasket
Source: Nonlinearity
Author: Ugo Bessi
Institution: Roma Tre University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7155089655