Geometry and its Applications

This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems.

This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as Maple(TM) and Mathematica®, as well as presentation of new results.

Contenu

Part I: Geometry.- The Ricci flow on some generalized Wallach spaces (N.A. Abiev, A. Arvanitoyeorgos, Y.G. Nikonorov, P. Siasos).- Gaussian mean curvature flow for submanifolds in space forms (A. Borisenko, V. Rovenski).- Cantor laminations and exceptional minimal sets in codimension one foliations (G. Hector).- Integral formulas in foliations theory (K. Andrzejewski, P. Walczak, V. Rovenski).- On prescribing the mixed scalar curvature of a foliations (V. Rovenski, L. Zelenko).- The partial Ricci flow for foliations (V. Rovenski).- Osculation in general (P. Walczak).- On stability of totally geodesic unit vector fields on three-dimensional Lie groups (A. Yampolsky).- Part II: Applications.- Rotational liquid film interacted with ambient gaseous media (I. Gaissinski, Y. Levy, V. Rovenski, V. Sherbaum).- On cycles and other geometric phenomena in phase portraits of some nonlinear dynamical systems (V. Golubyatnikov, Yu. A. Gaidov).- Remez-type inequality for smooth functions (Y. Iomdin).