Sentence examples for minimal surface of from inspiring English sources

Let S be a minimal surface of general type and let X be its canonical model.

Let X be the canonical model of a minimal surface of general type S with invariants (chi, K^2).

More precisely, let S be a minimal surface of general type and let X be its canonical model.

More generally, we show that any minimal surface of genus (1) which is Alexandrov immersed must be rotationally symmetric.

Second, in Section 3 we obtain an inequality on usual volume for any minimal surface of a Riemannian manifold with sectional curvature bounded above by a constant : (1.5).

In particular, there exists at least one embedded minimal surface of any given genus (g), and there are at least two such surfaces unless (g) is a prime number.

To see ring growth more clearly, we cut a minimal surface on one transverse side of each core using a stainless-steel razor blade.

In this section, we discuss uniqueness results for minimal surfaces of genus (0) and (1).

Given two minimal surfaces of general type (S, S') and their respective canonical models (X, X'), then.

We next discuss uniqueness theorems for minimal surfaces in (S^3), such as the work of Almgren on the genus (0) case, and our recent solution of Lawson's conjecture for embedded minimal surfaces of genus (1).

This changed dramatically in the late 1960s, when Lawson discovered an infinite family of embedded minimal surfaces of higher genus: (Lawson [37]) Given any pair of positive integers (m) and (k), there exists an embedded minimal surface (Sigma ) in (S^3) of genus (mk).