Spectrum of the Laplacian on manifolds with Spin(9) holonomy

• Autores: Kwan-Hang Lam
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 5-6, 2008, págs. 1167-1186
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n6.a8
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• Resumen

  • We consider noncompact complete manifolds with Spin(9) holonomy and proved an one end result and a splitting type theorem under different conditions on the bottom of the spectrum. We proved that any harmonic functions with finite Dirichlet integral must be Cayley-harmonic, which allowed us to conclude an one end result. In the second part, we established a splitting type theorem by utilizing the Busemann function.