Geometry on the group of Hamiltonian diffeomorphisms.
Geometry on the space of positive functions.
Geometry without topology as a new conception of geometry.
Geradenfamilien, Enveloppen und Evoluten.
Geradenkomplexe im Flaggenraum I.
Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects
We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.
Geschlossene äquiforme Bewegungen der Räume endlicher Dimension
Im ersten Teil des Artikels konstruiert der Verfasser eine geschlossene Bewegung, die an der Ähnlichkeitsgruppe definiert wird. Solche Bewegungen beschreiben periodisch sich wiederholende Prozesse für den Fall des beweglichen Gebildes, welches sich während der Bewegung ähnlich deformiert. Der zweite Teil verallgemeinert die geschlossene Bewebungen durch äquiforme Bewegungen, die so gegeben werden, dass eine Folge von erzeugenden Punkten dieselbe Bahnkurve beschreibt in der Art, dass die einzelnen...
Gheorge Titeica and affine differential geometry.
Gielisova transformace logaritmické spirály
Logaritmická spirála byla od okamžiku svého objevu studována z mnoha různých pohledů. Prvotní fascinace matematiků, z nichž někteří věnovali logaritmické spirále značnou část svého tvůrčího potenciálu, se postupně přenesla do dalších oblastí nejen přírodních věd a promítá se tak např. do fyziky, biologie, ale také různých inženýrských disciplín či architektury. Článek ukazuje, že logaritmická spirála popisovaná jako hladká křivka s exponenciálně rostoucím poloměrem může být transformována do řady...
Global boundedness, interior gradient estimates, and boundary regularity for the mean curvature equation with boundary conditions.
Global dynamics of media with microstructure.
Global eikonal condition for Lorentzian distance function in noncommutative geometry.
Global finite generating functions for field theory
We introduce an infinite-dimensional version of the Amann-Conley-Zehnder reduction for a class of boundary problems related to nonlinear perturbed elliptic operators with symmetric derivative. We construct global generating functions with finite auxiliary parameters, describing the solutions as critical points in a finite-dimensional space.
Global geometric structures associated with dynamical systems admitting normal shift of hypersurfaces in Riemannian manifolds.
Global Gronwall estimates for integral curves on Riemannian manifolds.
We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.
Global minimizers for axisymmetric multiphase membranes
We consider a Canham − Helfrich − type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous...
Global models of Riemannian metrics.
In this paper we give certain Riemannian metrics on the manifolds Sn-1 x S1 and Sn (n ≥ 2), which have the property to determine these manifolds, up to diffeomorphisms.The global expressions used for Riemannian metrics are based on the global expression for exterior forms studied in [4]. In [3] one finds certain metrics using global expressions that differ from the type we propose.To some extent, Theorem 3 is a generalization for metrics in an arbitrary dimension, of a theorem proved in [2] for...
Global Pinching Theorems for Even Dimensional Minimal Submanifolds in the Unit Sphere.
Global pinching theorems for minimal submanifolds in spheres
Let M be a compact submanifold with parallel mean curvature vector embedded in the unit sphere . By using the Sobolev inequalities of P. Li to get estimates for the norms of certain tensors related to the second fundamental form of M, we prove some rigidity theorems. Denote by H and the mean curvature and the norm of the square length of the second fundamental form of M. We show that there is a constant C such that if , then M is a minimal submanifold in the sphere with sectional curvature...
Global pinching theorems of submanifolds in spheres.