Invariant theory of variational problems on subspaces of a Riemannian manifold.
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Invariant theory of variational problems on subspaces of a Riemannian manifold. by Hanno Rund

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Published by Vandenhoeck & Ruprecht in Göttingen .
Written in English

Subjects:

  • Riemannian manifolds.,
  • Calculus of variations.,
  • Invariants.

Book details:

Edition Notes

Bibliography: p. [55]

SeriesHamburger mathematische Einzelschriften, n.F.,, Heft 5
Classifications
LC ClassificationsQA649 .R87
The Physical Object
Pagination54, [1] p.
Number of Pages54
ID Numbers
Open LibraryOL5356277M
LC Control Number72312012

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[13] H. Rund, Invariant theory of variational problems on subspaces of a Riemannian manifold, Hamburger Math. Einzelschriften No. 5, Zentralblatt MATH: Mathematical Reviews (MathSciNet): MRCited by: variational curves that generalizes the classical least squares problem to Riemannian manifolds. This generalization is also based on the formulation of higher-order variational problems, whose solutions are smooth curves minimizing the L2-norm of the covariant derivative of order k 1, that fit a given data set of points at given times. INVARIANT SUBSPACES 5 by these functions. They determine all nondecreasing functions of a real variable whose measure computes scalar products of elements of the space by integration. An invariant subspace theory applies to the difference–quotient transformation, taking a function F(z) of zinto the function [F(z)−F(0)]/z. In this paper we introduce a new approach to variational problems on the space Riem(M^n) of Riemannian structures (i.e. isometry classes of Riemannan metrics) on any fixed compact manifold M^n of dimension n >= 5. This approach often enables one to replace the considered variational problem on Riem(M^n) (or on some subset of Riem(M^n)) by the same problem but on spaces Riem(N^n) for Author: Alexander Nabutovsky, Shmuel Weinberger.

The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the “reduction to canonical form” of various objects of linear algebra or, what is. Noether – Invariant variational problems 3 On the other hand, I define the first variation δI for an arbitrary – not necessarily invariant – integral I, and convert it according to the rules of the calculus of variations by partial integration. LINEAR ALGEBRA: INVARIANT SUBSPACES 3 1. Invariant Subspaces Let V be a nonzero F-vector space. Let T2EndV be a linear endomorphism of V. A T-invariant subspace of V is a subspace W ˆV such that T(W) ˆW. Actually though we will just say \invariant subspace": throughout these notesFile Size: KB. case of single-variable variational problems would carry over to the case of functionals depending on surfaces. We focus on the case of two independent variables but refer to [1] for the case of more than two variables. Let F(x,y,z,p,q) be twice continuously differentiable with respect to all five variables, and consider J[z] = ZZ RFile Size: KB.

This book presents an innovative synthesis of methods used to study the problems of equivalence and symmetry that arise in a variety of mathematical fields and physical applications. It draws on a wide range of disciplines, including geometry, analysis, applied mathematics, and algebra. Dr. Invariant theory of variational problems on subspaces of a Riemannian manifold. Göttingen, Vandenhoeck & Ruprecht [©] (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Hanno Rund. A subspace ℳ ⊂ C / n is called invariant for the transformation A, or A invariant, if Ax ∈ ℳ for every vector x ∈ ℳ. In other words, ℳ is invariant for A means that the image of ℳ under A is contained in ℳ; Aℳ ⊂ ℳ. Trivial examples of invariant subspaces are {0} and C / n. Less trivial examples are the subspaces. Variational Theory for the Total Scalar Curvature Functional for Riemannian Metrics and Related Topics. Variational Theory for the Total Scalar Curvature Functional for Riemannian Metrics and Related Topics. Richard M. Schoen Mathematics Department Stanford University Stanford, CA