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Wolfe's Theorem in R^n

Show simple item record 2022-04-29T05:58:27Z 2022-04-29T05:58:27Z 2022-04-29
dc.title Wolfe's Theorem in R^n en
ethesis.faculty Matemaattis-luonnontieteellinen tiedekunta fi
ethesis.faculty Faculty of Science en
ethesis.faculty Matematisk-naturvetenskapliga fakulteten sv
ethesis.faculty.URI Helsingin yliopisto fi University of Helsinki en Helsingfors universitet sv
dct.creator Pim, Jonathan
dct.issued 2022 xx
dct.abstract Wolfe’s Theorem states that there is an isometric isomorphism between the space of flat k-cochains and the flat differential k-forms in R^n . The flat forms are the space of essentially bounded differential forms with an essentially bounded weak exterior derivative. The flat cochains are the dual space of the flat chains which are geometric objects based on finite linear combinations of k-simplices. In this sense, Wolfe’s Theorem connects geometry and analysis. After proving Wolfe’s Theorem, we give two corollaries: that the isomorphism from Wolfe’s Theorem can be concretely approximated by convolution with smooth mollifiers, and a version of Stokes’ Theorem for flat chains. Our method for proving Wolfe’s Theorem involves isometrically embedding the flat chains, as well as a predual of the flat forms, into the space of flat currents. By way of some approximation theorems in the space of flat currents, the images of these two embeddings coincide. Thus, the flat chains are isomorphic to that predual. This isomorphism lifts to their dual spaces giving Wolfe’s Theorem. en
dct.subject Wolfe’s Theorem
dct.subject Flat chains
dct.subject Flat forms
dct.subject Currents
dct.subject Differential k-forms
dct.subject k-vector fields
ethesis.isPublicationLicenseAccepted true
ethesis.language englanti fi
ethesis.language English en
ethesis.language engelska sv
ethesis.thesistype pro gradu -tutkielmat fi
ethesis.thesistype master's thesis en
ethesis.thesistype pro gradu-avhandlingar sv
dct.identifier.ethesis E-thesisID:5b4864bd-6448-4485-8fd6-a635d7e3ddc4
dct.identifier.urn URN:NBN:fi:hulib-202204291758
ethesis.facultystudyline Matematiikka fi
ethesis.facultystudyline Mathematics en
ethesis.facultystudyline Matematik sv
ethesis.mastersdegreeprogram Matematiikan ja tilastotieteen maisteriohjelma fi
ethesis.mastersdegreeprogram Master 's Programme in Mathematics and Statistics en
ethesis.mastersdegreeprogram Magisterprogrammet i matematik och statistik sv

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