✦ LIBER ✦

Scalar curvature on Sn and first spherical harmonics

✍ Scribed by Emmanuel Hebey

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 461 KB
Volume: 5
Category: Article
ISSN: 0926-2245
DOI: 10.1016/0926-2245(95)00007-q

No coin nor oath required. For personal study only.

✦ Synopsis

Let (S",go) be the unit sphere of Iw"+' endowed with its standard metric.

On one hand, according to the obstructions of Kazdan-Warner and Bourguignon-Ezin, the functions of t,he type 1 +hod, where h is a first spherical harmonic and where q4 is a conformal diffeomorphism of S", are not the scalar curvature of a metric conformal to go. On the other hand, we prove that we can associate to each function f a first spherical harmonic hf and a conformal diffeomorphism d such that fhf o q4 is the scalar curvature of a metric conformal to go. When n = 3, if f is symmetric at one of its maximum points, there exists hf a first spherical harmonic such that fhf is the scalar curvature of a metric conformal to go.

📜 SIMILAR VOLUMES

On the Symmetric Scalar Curvature Proble

On the Symmetric Scalar Curvature Problem on Sn

✍ Antonio Ambrosetti; Andrea Malchiodi 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 162 KB

We discuss some existence results dealing with the scalar curvature problem on S n in the presence of various symmetries.

On symmetric finsler spaces ofHp-scalar

On symmetric finsler spaces ofHp-scalar curvature and scalar curvature

✍ B. B. Sinha; A. Ram 📂 Article 📅 1986 🏛 Springer Netherlands 🌐 English ⚖ 386 KB

Horizontal curvature on a spherical Eart

Horizontal curvature on a spherical Earth

✍ C. H. B. Priestley 📂 Article 📅 1948 🏛 John Wiley and Sons 🌐 English ⚖ 133 KB

On the efficient calculation of ordinary

On the efficient calculation of ordinary and generalized spherical harmonics

✍ Guy Masters; Keith Richards-Dinger 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 162 KB

On spherical harmonics expansion type mo

On spherical harmonics expansion type modelsfor electron–phonon collisions

✍ J.-P. Bourgade 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 219 KB

## Abstract In this paper, we give the rigorous derivation of a diffusion model for semiconductor devices, the starting point being a microscopic description of electron transport by means of a kinetic equation of Boltzmann type. The limit of a small mean free path at a large time leads to a diffus

On the Regularity of Harmonic Functions

On the Regularity of Harmonic Functions and Spherical Harmonic Maps Defined on Lattices

✍ Lawrence E. Thomas 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 140 KB

A growth lemma for certain discrete symmetric Laplacians defined on a lattice Z d δ = δZ d ⊂ R d with spacing δ is proved. The lemma implies a De Giorgi theorem, that the harmonic functions for these Laplacians are equi-Hölder continuous, δ → 0. These results are then applied to establish regularity