| dc.date.accessioned |
2022-04-29T05:58:27Z |
|
| dc.date.available |
2022-04-29T05:58:27Z |
|
| dc.date.issued |
2022-04-29 |
|
| dc.identifier.uri |
http://hdl.handle.net/123456789/40305 |
|
| 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 |
http://data.hulib.helsinki.fi/id/8d59209f-6614-4edd-9744-1ebdaf1d13ca |
|
| ethesis.university.URI |
http://data.hulib.helsinki.fi/id/50ae46d8-7ba9-4821-877c-c994c78b0d97 |
|
| ethesis.university |
Helsingin yliopisto |
fi |
| ethesis.university |
University of Helsinki |
en |
| ethesis.university |
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.URI |
http://data.hulib.helsinki.fi/id/languages/eng |
|
| 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 |
| ethesis.thesistype.URI |
http://data.hulib.helsinki.fi/id/thesistypes/mastersthesis |
|
| 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.facultystudyline.URI |
http://data.hulib.helsinki.fi/id/SH50_050 |
|
| 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 |
| ethesis.mastersdegreeprogram.URI |
http://data.hulib.helsinki.fi/id/MH50_001 |
|
