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Some Old and New Results in Spectral Geometry of the Laplacian
Speaker: Dr. Cristian Enache, Assistant Professor of Mathematics, American University of Sharjah. Research area: PDEs, Applicable Analysis, Calculus of Variations
Abstract: The problem of optimizing a domain dependent functional, while keeping a certain domain`s measure fixed (such as, for instance, its volume/area/perimeter/width/conformal radius, etc.), is called an isoperimetric problem. The isoperimetric problems have a long history in mathematics dating back to the Greeks and Dido’s problem, i.e., the classical isoperimetric inequality in Euclidean geometry. With the introduction of the calculus of variations in the 17th century, isoperimetric inequalities found their way into mathematical physics. Among the isoperimetric problems, in this talk I plan to present the ones linking the shape of a domain/drum to the sequence of “its” eigenvalues/frequencies.