# Weak convergence of currents and cancellation

## Related Articles

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We use the theory of rectifiable metric spaces to define a Dirichlet energy of Lipschitz functions defined on the support of integral currents. This energy is obtained by integration of the square of the norm of the tangential derivative, or equivalently of the approximate local dilatation, of...

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By Gromov's compactness theorem for metric spaces, every uniformly compact sequence of metric spaces admits an isometric embedding into a common compact metric space in which a subsequence converges with respect to the Hausdorff distance. Working in the class of oriented k-dimensional Riemannian...

- Lipschitz Functions and Ekeland's Theorem. Beer, Gerald; Ceniceros, Jose // Journal of Optimization Theory & Applications;Mar2012, Vol. 152 Issue 3, p652
As shown by F. Sullivan (Proc. Am. Math. Soc. 83:345-346, ), validity of the weak Ekeland variational principle implies completeness of the underlying metric space. In this note, we show that what really forces completeness in Sullivan's argument is an even simpler geometric property of lower...

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We consider the uniqueness of Ricci flow with the initial curvature bounded from above, but not necessarily bounded from below, on a 2-dimensional complete noncompact manifold.

- Unavoidable sigma-porous sets. // Journal of the London Mathematical Society;Oct2007, Vol. 76 Issue 2, p467
We prove that every separable metric space which admits an â„“1-tree as a Lipschitz quotient has a Ïƒ-porous subset which contains every Lipschitz curve up to a set of one-dimensional Hausdorff measure zero. This applies to any Banach space containing â„“1. We also obtain an...

- On HÃ¶lder maps of cubes. Shchepin, E. V. // Mathematical Notes;Jun2010, Vol. 87 Issue 5/6, p757
A map of metric spaces f: X â†’ Y satisfying the inequality for some C and Î± and all x, y âˆˆ X is called a HÃ¶lder map with exponent Î±. V. I. Arnold posed the following problem: Does there exist a HÃ¶ldermap from the square onto the cube with exponent 2/3? The firstmain...

- Tikhonov regularization of metrically regular inclusions. Gaydu, Micha�l; Geoffroy, Michel // Positivity;Jun2009, Vol. 13 Issue 2, p385
We present a Tikhonov regularization method for inclusions of the form $$T(x) \ni 0$$ where T is a set-valued mapping defined on a Banach space that enjoys metric regularity properties. We investigate, subsequently, the case when the mapping T is metrically regular, strongly metrically regular,...

- ON FIXED POINTS OF GENERALIZED SET-VALUED CONTRACTIONS. BENAHMED, S.; AZÉ, D. // Bulletin of the Australian Mathematical Society;Feb2010, Vol. 81 Issue 1, p16
Using a variational method introduced in [D. AzÃ© and J.-N. Corvellec, 'A variational method in fixed point results with inwardness conditions', Proc. Amer. Math. Soc. 134(12) (2006), 3577-3583], deriving directly from the Ekeland principle, we give a general result on the existence of a fixed...

- On Some Lacunary Generalized Difference Sequence Spaces Defined by a Modulus Function in a Locally Convex Space. Bhardwaj, Vinod K.; Bala, Indu // Southeast Asian Bulletin of Mathematics;2009, Vol. 33 Issue 4, p665
In this paper, we introduce some new lacunary generalized difference sequence spaces defined by a modulus function in a locally convex Hausdorff topological linear space whose topology is determined by a finite set Q of seminorms. Various algebraic and topological properties of these spaces, and...