All papers appearing in this volume are original research articles and have not been published elsewhere. They meet the requirements that are necessary for publication in a good quality primary journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M. Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A. Miernowski, W.Mozgawa: Isoptics of a strictly convex curve. -F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez, O.J.Garay, P.Lucas: On a certain class of conformally flat Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with non-negative Ricci operator. -B.Hajduk: On the obstruction group toexistence of Riemannian metrics of positive scalar curvature. -U.Hammenstaedt: Compact manifolds with 1/4-pinched negative curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of stable vector bundles over Riemannian surfaces. - O.Kowalski, F.Tricerri: A canonical connection for locally homogeneous Riemannian manifolds. -M.Kozlowski: Some improper affine spheres in A3. -R.Kusner: A maximum principle at infinity and the topology of complete embedded surfaces with constant mean curvature. -Anmin Li: Affine completeness and Euclidean completeness. -U.Lumiste: On submanifolds with parallel higher order fundamental form in Euclidean spaces. -A.Martinez, F.Milan: Convex affine surfaces with constant affine mean curvature. -M.Min-Oo, E.A.Ruh, P.Tondeur: Transversal curvature and tautness for Riemannian foliations. -S.Montiel, A.Ros: Schroedinger operators associated to a holomorphic map. -D.Motreanu: Generic existence of Morse functions on infinite dimensional Riemannian manifolds and applications. -B.Opozda: Some extensions of Radon's theorem.

Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory. Here, not only Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory.

This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e., submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object."