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dc.contributor.advisor Hardt, Robert M.
dc.creatorMeng, Zheng
dc.date.accessioned 2009-06-04T08:21:29Z
dc.date.available 2009-06-04T08:21:29Z
dc.date.issued 2005
dc.identifier.urihttps://hdl.handle.net/1911/18846
dc.description.abstract We study here some geometric variational problems motivated by the modeling of plants' growth. In Chapter 2, we conclude the general existence of an area minimizing surface with given boundary on two parallel hyperplanes and the constraint that the intersection of the surface with each hyperplane parallel to these of the boundary encloses the same area. In Chapter 3, we study the area minimizing surface in R 3 whose intersection with each of the hyperplanes R 2 x {h}, h ∈ [0, 1] encloses a prescribed area. We conclude that, up to a translation, the minimizer exists and is invariant under revolution. In Chapter 4, as a specific case of the problem in Chapter 2, the minimizing surface bounded by two parallel circles of the same size is studied carefully. We conclude that such an area minimizing surface is the skewed cylinder determined by the two circles. In Chapter 5, we study an analogous energy minimizing problem in PDE with a boundary constraint and a cross-sectional constraint on the L1 norm over a rectangular region. The even terms and the conditions for the odd terms in the Fourier expansion of the energy minimizer are given.
dc.format.extent 57 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
dc.title Geometric variational problems with cross-sectional constraints
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation Meng, Zheng. "Geometric variational problems with cross-sectional constraints." (2005) Diss., Rice University. https://hdl.handle.net/1911/18846.


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