Sentence examples for minimal surface case from inspiring English sources

In this case, the relative isoperimetric inequality can be extended to the hyperbolic space, and to a minimal submanifold case (not necessarily a minimal surface case).

A circle is the most obvious example of a minimal surface.

In 1966, Almgren proved the following uniqueness theorem in the genus (0) case: (Almgren [2]) The equator is the only immersed minimal surface in (S^3) of genus (0) (up to rigid motions in (S^3)).

In this case, Marques and Neves show that there exists an embedded minimal surface (tilde{Sigma }) with area (mathrm{area} tilde{Sigma }) = Lambda ).

The minimized quantity of boundary molecules results in a minimal surface area.

In our test cases we may achieve exponential convergence in the approximation of the minimal surface as the polynomial degree increases, but the rate of convergence greatly differs with different choices of mesh update algorithms.

In the case of the extruded nanofibers, prepared as described, the aminolysis reaction using either propargylamine or hexamethylene diamine showed minimal surface modification under mild reaction conditions.

Geodesic structures are perfect for covering the maximum enclosed volume with the minimal surface area.

(Sigma ) is a minimal surface.

In this paper, we combine the geodesic and minimal surface.

Minimal surface binding was observed by healthy cells.