Details
| Original language | English |
|---|---|
| Journal | Potential analysis |
| Early online date | 28 Oct 2023 |
| Publication status | E-pub ahead of print - 28 Oct 2023 |
Abstract
We present an explicit form of the subelliptic heat kernel of the intrinsic sublaplacian Δsub5 induced by a rank 5 trivializable subriemannian structure on the Euclidean seven dimensional sphere S7 . This completes the heat kernel analysis of trivializable subriemannian structures on S7 induced by a Clifford module action on R8 . As an application we derive the spectrum of Δsub5 and the Green function of the conformal sublaplacian in an explicit form.
Keywords
- Green kernel, Heat kernel, Sublaplacian, Subriemannian geometry
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Potential analysis, 28.10.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Rank 5 Trivializable Subriemannian Structure on S7 and Subelliptic Heat Kernel
AU - Bauer, Wolfram
AU - Laaroussi, Abdellah
AU - Tarama, Daisuke
N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL. The first and second author have been supported by the priority programm SPP 2026 geometry at infinity of Deutsche Forschungsgemeinschaft (project number BA 3793/6-1). The third author has been supported by JSPS KAKENHI, grant number JP19K14540, JP22H01138, JP23H04481. This work was partially supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
PY - 2023/10/28
Y1 - 2023/10/28
N2 - We present an explicit form of the subelliptic heat kernel of the intrinsic sublaplacian Δsub5 induced by a rank 5 trivializable subriemannian structure on the Euclidean seven dimensional sphere S7 . This completes the heat kernel analysis of trivializable subriemannian structures on S7 induced by a Clifford module action on R8 . As an application we derive the spectrum of Δsub5 and the Green function of the conformal sublaplacian in an explicit form.
AB - We present an explicit form of the subelliptic heat kernel of the intrinsic sublaplacian Δsub5 induced by a rank 5 trivializable subriemannian structure on the Euclidean seven dimensional sphere S7 . This completes the heat kernel analysis of trivializable subriemannian structures on S7 induced by a Clifford module action on R8 . As an application we derive the spectrum of Δsub5 and the Green function of the conformal sublaplacian in an explicit form.
KW - Green kernel
KW - Heat kernel
KW - Sublaplacian
KW - Subriemannian geometry
UR - http://www.scopus.com/inward/record.url?scp=85175079025&partnerID=8YFLogxK
U2 - 10.1007/s11118-023-10110-8
DO - 10.1007/s11118-023-10110-8
M3 - Article
AN - SCOPUS:85175079025
JO - Potential analysis
JF - Potential analysis
SN - 0926-2601
ER -