No description available.

No description available.

Nesta dissertação foram discutidas abordagens do problema isoperimétrico que podem ser aplicadas no ensino médio e para alunos de Licenciatura plena em Matemática. Foi realizada inicialmente uma abordagem histórica e posteriormente a discussão de casos particulares e gerais de desigualdade isoperimétrica tanto no plano como no espaço. A abordagem principal deste texto é no plano, no qual foram analisadas as áreas dos triângulos, quadriláteros e polígonos regulares dado um perímetro fixo. / In this dissertation isoperimetric problem approaches were discussed that can be applied in high school and full degree students in mathematics. It was initially performed a historical approach and then the discussion of individual and general cases of isoperimetric inequality both in the plane and in space . The main approach of this text is in the plan, in which the areas of the triangles were analyzed , quadrilaterals and regular polygons given a fixed perimeter.

Nesta dissertação foram discutidas abordagens do problema isoperimétrico que podem ser aplicadas no ensino médio e para alunos de Licenciatura plena em Matemática. Foi realizada inicialmente uma abordagem histórica e posteriormente a discussão de casos particulares e gerais de desigualdade isoperimétrica tanto no plano como no espaço. A abordagem principal deste texto é no plano, no qual foram analisadas as áreas dos triângulos, quadriláteros e polígonos regulares dado um perímetro fixo. / In this dissertation isoperimetric problem approaches were discussed that can be applied in high school and full degree students in mathematics. It was initially performed a historical approach and then the discussion of individual and general cases of isoperimetric inequality both in the plane and in space . The main approach of this text is in the plan, in which the areas of the triangles were analyzed , quadrilaterals and regular polygons given a fixed perimeter.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 79-83). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 79-83). Also available on the Internet.

No description available.

We study two related inequalities that arise in Harmonic Analysis: restriction type inequalities and isoperimetric inequalities. The (Lp, Lq) Restriction type inequalities have been the subject of much interest since they were first conceived in the 1960s. The classical restriction type inequality involving surfaces of non-vanishing curvature is only fully resolved in two dimensions and there have been a lot of recent developments to establish the conjectured (p,q) range in higher dimensions. However, it also interesting to consider what can be said for curves where the curvature does vanish. In particular we build upon a restriction result for homogeneous polynomial surfaces, using what is considered the natural weight - the one induced by the affine curvature of the surface. This is known to hold with a non-universal constant which depends in some way on the coefficients of the polynomial. In this dissertation we shall quantify that relationship. Restriction estimates (for curves or surfaces) using the affine curvature weight can be shown to lead to an affine isoperimetric inequality for such curves or surfaces. We first prove, directly, this inequality for polynomial curves, where the constant depends only on the degree of the underlying polynomials. We then adapt this method, to prove an isoperimetric inequality for a wide class of curves, which includes curves for which a restriction estimate is not yet known. Next we state and prove an analogous result of the relative affine isoperimetric inequality, which applies to unbounded convex sets. Lastly we demonstrate that this relative affine isoperimetric inequality for unbounded sets is in fact equivalent to the classical affine isoperimetric inequality.

A introduction to metacalibration methods and their application. This includes a new proof of the double bubble conjecture, new results in the area of equitent problems (isoperimetric problems with boundary), and comments on a mapping conjecture.

Lin, Jessey. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 79-80). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.