Displaying similar documents to “An Overview of the Proof of the Splitting Theorem in Spaces with Non-Negative Ricci Curvature”

Change of variables formula under minimal assumptions

Piotr Hajłasz (1993)

Colloquium Mathematicae

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In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We...

An intrinsic definition of the Colombeau generalized functions

Jiří Jelínek (1999)

Commentationes Mathematicae Universitatis Carolinae

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A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a 𝒞 manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.