Format:
Online-Ressource
ISSN:
2391-5455
Content:
Abstract: Gaussian solitons are important examples in the theory of Riemannian measure space. In the first part, we explicitly characterize the first eigenfunctions of the drift Laplacian in a Gaussian shrinking soliton, which shows that apart from each coordinate function, other first eigenfunctions must involve exponential functions and the so-called error functions. Moreover, the second eigenfunctions are also described. In the second part, we discuss the corresponding issues in Finsler Gaussian shrinking solitons, which is a natural generalization of Gaussian shrinking solitons. For the first eigenfunction, we complement an example to show that if a coordinate function is a first eigenfunction, then the Finsler Gaussian shrinking soliton must be a Euclidean measure space. For the second eigenfunction, we give some necessary and sufficient conditions for these spaces to be Euclidean measure spaces.
In:
volume:21
In:
number:1
In:
year:2023
In:
extent:10
In:
Open mathematics, Berlin : de Gruyter, 2015-, 21, Heft 1 (2023) (gesamt 10), 2391-5455
Language:
English
DOI:
10.1515/math-2023-0167
URN:
urn:nbn:de:101:1-2024010213064195498129
URL:
https://doi.org/10.1515/math-2023-0167
URL:
https://nbn-resolving.org/urn:nbn:de:101:1-2024010213064195498129
URL:
https://d-nb.info/1314922793/34