Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01ht24wn18p
DC FieldValueLanguage
dc.contributor.authorYin, Gloria-
dc.date.accessioned2018-08-17T19:05:34Z-
dc.date.available2018-08-17T19:05:34Z-
dc.date.created2018-05-03-
dc.date.issued2018-08-17-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01ht24wn18p-
dc.description.abstractWe explore the notions of Gaussian curvature and mean curvature on discrete surfaces. In the introduction, we define discrete surfaces rigorously and introduce relevant notions of curvature on smooth surfaces. Then, in section 2, we use the local version of the smooth Gauss-Bonnet theorem to define Gaussian curvature on discrete surfaces. Using this discrete Gaussian curvature, we are able to find a discrete analogy for the global Gauss-Bonnet theorem. Next, in section 3, we use a discrete analogy of the first variation of area to define mean curvature on discrete surfaces. We are then able to define a discrete minimal surface as one that is critical for area amongst continuous piecewise linear variations of discrete surfaces which preserve the boundary conditions. Finally, we consider an explicit example of a discrete catenoid which is a discrete minimal surface and which converges to a smooth catenoid in increasing the number of vertices in the discrete surface.en_US
dc.format.mimetypeapplication/pdf-
dc.language.isoenen_US
dc.titleCurvature on Discrete Surfacesen_US
dc.typePrinceton University Senior Theses-
pu.date.classyear2018en_US
pu.departmentMathematicsen_US
pu.pdf.coverpageSeniorThesisCoverPage-
pu.contributor.authorid961039130-
pu.certificateApplications of Computing Programen_US
Appears in Collections:Mathematics, 1934-2020

Files in This Item:
File Description SizeFormat