Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Non-immersion theorem for a class of hyperbolic manifolds
1998
Abstract It is proved that a non-simply-connected complete hyperbolic manifold cannot be isometrically immersed in a Euclidean space with a flat normal connection. In particular, the complete hyperbolic manifold M n with π 1 ( M ) ≠ 0 cannot be isometrically immersed in R 2 n − 1 .
Comparison theorems for the volume of a complex submanifold of a Kaehler manifold
1990
LetM be a Kaehler manifold of real dimension 2n with holomorphic sectional curvatureK H≥4λ and antiholomorphic Ricci curvatureρ A≥(2n−2)λ, andP is a complex hypersurface. We give a bound for the quotient (volume ofP)/(volume ofM) and prove that this bound is attained if and only ifP=C P n−1(λ) andM=C P n(λ). Moreover, we give some results on the volume of of tubes aboutP inM.
Techniques in the Theory of Local Bifurcations: Cyclicity and Desingularization
1993
A fundamental open question of the bifurcation theory of vector fields in dimension 2 is whether the number of locally bifurcating limit cycles in an analytic unfolding is bounded, or more precisely, whether any limit periodic set has finite cyclicity. In these notes we introduce several techniques for attacking this question: asymptotic expansion of return maps, ideal of coefficients, desingularization of parametrized families. Moreover, because of their practical interest, we present some partial results obtained by these techniques.
Retractive product spaces
1990
Abstract A completely regular Hausdorff space X is called retractive if there is a retraction from βX onto βX \ X . A product space is retractive if and only if all factors are compact but one which is retractive.
On the structure of the set of solutions of nonlinear equations
1971
Let T be a mapping from a subset of a Banach space X into a Banach space Y. The present paper investigates the nature of the set of solutions of the equation T(x) = y for a given y E Y, i.e. when T-l(y) # 0 ? What are the topological properties of T-l(y)? A prototype for an answer to these questions is given by Peano existence theorem on the connectedness of the set of solutions of an ordinary differential equation in the real case. In its general setting, this problem was first attacked by Aronszajn [l] and Stampacchia [l 11; recently, by Browder-Gupta [5], Vidossich [12] and, above all, Browder [3, Sec. 51 who gives several interesting results in an excellent treatment. Customary, the str…
Sharp inequalities via truncation
2003
Abstract We show that Sobolev–Poincare and Trudinger inequalities improve to inequalities on Lorentz-type scales provided they are stable under truncations.
Some Multiplicative Inequalities for Inner Products and of the Carlson Type
2008
We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities. Validerad; 2008; Bibliografisk uppgift: Paper id:: 890137; 20080826 (ysko)
In between the inequalities of Sobolev and Hardy
2015
We establish both sufficient and necessary conditions for the validity of the so-called Hardy-Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev inequalities and the (weighted) Hardy inequalities. The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions.
From metric spaces to partial metric spaces
2013
Motivated by experience from computer science, Matthews (1994) introduced a nonzero self-distance called a partial metric. He also extended the Banach contraction principle to the setting of partial metric spaces. In this paper, we show that fixed point theorems on partial metric spaces (including the Matthews fixed point theorem) can be deduced from fixed point theorems on metric spaces. New fixed point theorems on metric spaces are established and analogous results on partial metric spaces are deduced. MSC:47H10, 54H25.
Singular levels and topological invariants of Morse Bott integrable systems on surfaces
2016
Abstract We classify up to homeomorphisms closed curves and eights of saddle points on orientable closed surfaces. This classification is applied to Morse Bott foliations and Morse Bott integrable systems allowing us to define a complete invariant. We state also a realization Theorem based in two transformations and one generator (the foliation of the sphere with two centers).