2024/01/10 by Bennett Palmer, Palmer, Bennett, Álvaro Pámpano +1 · 1 citation
Immunology and Microbiology · Mathematics · Medicine · #Biomedical Research and Pathophysiology #Differential Geometry (math.DG) #FOS: Mathematics #Navier-Stokes equation solutions #Phagocytosis and Immune Regulation
paper · pdf · doi:10.48550/arxiv.2401.05285
openalex publication_date 2024/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [12], the authors studied a particular class of equilibrium solutions of the Helfrich energy which satisfy a second order condition called the reduced membrane equation. In this paper we develop and apply a second variation formula for the Helfrich energy for this class of surfaces. The reduced membrane equation also arises as the Euler-Lagrange equation for the area of surfaces under the action of gravity in the three dimensional hyperbolic space. We study the second variation of this functional for a particular example.