Spectral Determinant on Euclidean Isosceles Triangle Envelopes

Autor:	Victor Kalvin
Rok vydání:	2021
Předmět:	Differential geometry Mathematical analysis Isosceles triangle Euclidean geometry Geometry and Topology Function (mathematics) Computer Science::Computational Geometry Equilateral triangle Laplace operator Critical point (mathematics) Mathematics Envelope (waves)
Zdroj:	The Journal of Geometric Analysis. 31:12347-12374
ISSN:	1559-002X 1050-6926
DOI:	10.1007/s12220-021-00717-x
Popis:	We study extremal properties of the determinant of Friedrichs selfadjoint Laplacian on the Euclidean isosceles triangle envelopes of fixed area as a function of angles. We deduce an explicit closed formula for the determinant. Small-angle asymptotics show that the determinant grows without any bound as an angle of a triangle envelope goes to zero. We prove that the equilateral triangle envelope (the most symmetrical geometry) always gives rise to a critical point of the determinant and finds the critical value. When the area is below a certain value (approximately 1.92), the equilateral envelope minimizes the determinant. When the area exceeds this value, the equilateral envelope is a local maximum of the determinant.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::57078227bcea41d83e54cb701bf0b948 https://doi.org/10.1007/s12220-021-00717-x Zobrazit plný text záznamu Full text from SpringerLink