Overview

This 2001 book is devoted to an invariant multidimensional process of recovering a function from its derivative. It considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. A typical example is the flux of a continuous vector field. A very general Gauss-Green theorem follows from the sufficient conditions for the derivability of the flux. Since the setting is invariant with respect to local lipeomorphisms, a standard argument extends the Gauss-Green theorem to the Stokes theorem on Lipschitz manifolds. In addition, the author proves the Stokes theorem for a class of top-dimensional normal currents - a first step towards solving a difficult open problem of derivation and integration in middle dimensions. The book contains complete and detailed proofs and will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas.

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9780511574764

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Review of the hardback: '…warmly recommended to researchers and advanced graduate students …'. József Németh, Acta Sci. Math. Review of the hardback: '…I warmly recommended this book …'. Thierry de Pauw, Bulletin of the Belgian Mathematical Society Review of the hardback: ' … written by one of the leading specialists in this field.' EMS Review of the hardback: 'Readers with a good background in analysis will find this an illuminating account.' Mathematika

Review of the hardback: '...warmly recommended to researchers and advanced graduate students ...'. Jozsef Nemeth, Acta Sci. Math. Review of the hardback: '...I warmly recommended this book ...'. Thierry de Pauw, Bulletin of the Belgian Mathematical Society Review of the hardback: ' ... written by one of the leading specialists in this field.' EMS Review of the hardback: 'Readers with a good background in analysis will find this an illuminating account.' Mathematika

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