Sentence examples for minimal surface equations from inspiring English sources

The global existence of solutions to timelike minimal surface equations with slow decay initial value in two space dimensions and three space dimensions will be proved in Section 3 and Section 4, respectively.

In this paper, we prove that the global existence of solutions to timelike minimal surface equations having arbitrary co-dimension with slow decay initial data in two space dimensions and three space dimensions, provided that the initial value is suitably small.

The key issue is to deform the surface (Sigma _{m,zeta }) to an exact solution of the minimal surface equation.

In this survey, we discuss various aspects of the minimal surface equation in the three-sphere (S^3).

In this way, one obtains a family of approximate solutions of the minimal surface equation, and Kapouleas and Yang showed that these surfaces can be deformed to exact solutions of the minimal surface equation by means of the implicit function theorem.

The surface parametrized by X c, τ + w n c is minimal if and only if the function w satisfies the minimal surface equation 2 H w = 1 τ 2 L C w + Q τ ( w ) = 0, (10).

The function u m satisfies the minimal surface equation, which has the following form: 2 H u = | x | 4 τ div ( ∇ u ( 1 + | x | 4 | ∇ u | 2 ) 1 / 2 ) = 0. (5).

But we cannot find a minimal surface which satisfies the equality.

Our methodology makes use of a direct relationship between form and force, offered by the Laplace Young equation that describes shapes of minimal surface membranes, such as soap films.

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

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