Spectrum Estimates and Applications to Geometry

Abstract

In 1867, E. Beltrami (Ann Mat Pura Appl 1(2):329–366, 1867, [12]) introduced a second order elliptic operator on Riemannian manifolds, defined by $$\Delta ={\mathrm{{div}\,}}\circ {{\mathrm {grad}\,}}$$ , extending the Laplace operator on $$\mathbb {R}^{n}$$ , called the Laplace–Beltrami operator. The Laplace–Beltrami operator became one of the most important operators in Mathematics and Physics, playing a fundamental role in differential geometry, geometric analysis, partial differential equations, probability, potential theory, stochastic process, just to mention a few. It is in important in various differential equations that describe physical phenomena such as the diffusion equation for the heat and fluid flow, wave propagation, Laplace equation and minimal surfaces.

Locations

• Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano) - View - PDF
• Institutional Research Information System University of Turin (University of Turin) - View - PDF
• Atlantis Press eBooks - View