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In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint.
Minimal surface has zero curvature at every point on the surface. Since a surface surrounded by a boundary is minimal if it is an area minimizer, the study of minimal surface has arised many interesting applications in other fields in science, such as soap films. In this book, we have included the lecture notes of a seminar course
6 de jun. de 2020 · History. Minimal surface. A surface for which the mean curvature $ H $ is zero at all points. The first research on minimal surfaces goes back to J.L. Lagrange (1768), who considered the following variational problem: Find a surface of least area stretched across a given closed contour.
En matemáticas, una superficie minimal es un elemento bidimensional que localmente minimiza su área. Esto es equivalente a (véase infra: Definiciones) tener una curvatura media nula.
30 de may. de 2024 · Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, (1+h_v^2)h_(uu)-2h_uh_vh_(uv)+(1+h_u^2)h_(vv)=0 (1) (Gray 1997, p. 399).
19 de dic. de 2019 · Minimal surfaces are shapes that minimise area within a given boundary or along a given loop. Learn about their origins, properties and applications, and how mathematicians are still exploring them today.
15 de ago. de 2013 · Lectures on Minimal Surface Theory. An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute. 46 pages, 6 figures.
