By Steven G. Krantz
This booklet brings into concentration the synergistic interplay among research and geometry by means of analyzing various subject matters in functionality thought, actual research, harmonic research, a number of advanced variables, and team activities. Krantz's process is influenced through examples, either classical and smooth, which spotlight the symbiotic dating among research and geometry. making a synthesis between a number of other themes, this publication turns out to be useful to researchers in geometry and research and will be of curiosity to physicists, astronomers, and engineers in yes components. The publication is predicated on lectures offered at an NSF-CBMS nearby convention held in may possibly 1992.
By Kevin McGerty
By Johannes C C Nitsche
This 1989 monograph bargains with parametric minimum surfaces in Euclidean area. the writer offers a extensive survey which extends from the classical beginnings to the present state of affairs while highlighting the various subject's major positive aspects and interspersing the mathematical improvement with pertinent ancient comments. The presentation is entire and is complemented through a bibliography of approximately 1600 references. The cautious expository sort and emphasis on geometric points are super precious. furthermore, within the years top as much as the e-book of this publication, the speculation of minimum surfaces used to be discovering expanding program to different parts of arithmetic and the actual sciences making sure that this account will attract non-specialists to boot
By Steven Zelditch
This paintings is worried with a couple of twin asymptotics difficulties on a finite-area hyperbolic floor. the 1st challenge is to figure out the distribution of closed geodesics within the unit tangent package deal. The author's effects supply a quantitative shape to Bowen's equidistribution conception: they refine Bowen's theorem a lot because the top geodesic theorem on hyperbolic quotients refines the asymptotic formulation for the variety of closed geodesics of size lower than T. specifically, the writer offers a expense of equidistribution when it comes to low eigenvalues of the Laplacian. the second one challenge is to figure out the distribution of eigenfunctions (in microlocal feel) within the unit tangent package. the most outcome right here (which is required for the equidistribution conception of closed geodesics) is an explanation of a signed and averaged model of the suggest Lindelof speculation for Rankin-Selberg zeta features. the most instrument used here's a generalization of Selberg's hint formulation.
By Pogorelov A.V.
By Joseph C. Varilly, Hector Figueroa, Jose M. Gracia-Bondia
This quantity covers a variety of subject matters together with resources of noncommutative geometry; basics of noncommutative topology; K-theory and Morita equivalance; noncommutative integrodifferential calculus; noncommutative Riemannian spin manifolds; commutative geometrics; tori; facts of Connes' Riemannian spin theorem; moment quantization; noncommutative quantum box conception; C*-algebras; Hopf algebras; Clifford algebras; Moyal algebras; pseudodifferential operators; the commutative Chern personality theorem.
By Kentaro Yano
By Lugo G.
By G. G. Magaril-Ilyaev, V. M. Tikhomirov
This e-book is an advent to convex research and a few of its purposes. It begins with uncomplicated thought, that's defined in the framework of finite-dimensional areas. the one necessities are uncomplicated research and easy geometry. the second one bankruptcy provides a few purposes of convex research, together with difficulties of linear programming, geometry, and approximation. specific cognizance is paid to functions of convex research to Kolmogorov-type inequalities for derivatives of services in a single variable. bankruptcy three collects a few effects on geometry and convex research in infinite-dimensional areas. A complete advent written "for newcomers" illustrates the basics of convex research in finite-dimensional areas.
By Norman Steenrod
Fibre bundles, now an essential component of differential geometry, also are of significant significance in sleek physics - corresponding to in gauge conception. This publication, a succinct advent to the topic by means of renown mathematician Norman Steenrod, used to be the 1st to provide the topic systematically.It starts off with a normal creation to bundles, together with such issues as differentiable manifolds and overlaying areas. the writer then offers short surveys of complex themes, resembling homotopy thought and cohomology conception, ahead of utilizing them to check additional houses of fibre bundles. the result's a vintage and undying paintings of serious software that might entice severe mathematicians and theoretical physicists alike.