Cauchy-Riemann inequalities on 2-spheres of $\mathbb{R}^7$

Autor:	Salavessa, Isabel M. C.
Rok vydání:	2011
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Spectral Theory 53C42 53C38 58E12 35J20 47A75
Druh dokumentu:	Working Paper
Popis:	We prove that an integral Cauchy-Riemann inequality holds for any pair of smooth functions $(f,h)$ on the 2-sphere $\mathbb{S}^2$, and equality holds iff $f$ and $h$ are related $\lambda_1$-eigenfunctions. We extend such inequality to 4-tuples of functions, only valid on the $L^2$-orthogonal complement of a suitable nonzero finite dimensional space of functions. As a consequence we prove that 2-spheres are not $\Omega$-stable surfaces with parallel mean curvature in $\mathbb{R}^7$ for the associative calibration $\Omega$. Comment: 24 pages. LaTex2e V2: we correct some minor misprints. Remove a nonsense sentence in corollary 1.1, and correct a reference
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1105.3153 Zobrazit plný text záznamu View this record from Arxiv