Sentence examples for manifold without from inspiring English sources

Let \((M,g)\) be a compact Riemannian manifold without boundary.

Let M be a compact Riemannian manifold without boundary.

Abstract: Let $(M,g)$ be a compact Riemannian manifold without boundary.

Uneven distributions were observed for high mass flow rates at the cathode manifold without baffle.

Finally, we derive estimates for sums of squares of eigenvalues on a compact Riemannian manifold without boundary.

Furthermore, we show how the framework can be implemented in the general-purpose coordination language MANIFOLD without the need for using special architectures or real-time languages.

It is shown here, that for any C2, compact, 2-manifold without boundary, which is embedded in R3, there exists a piecewise linear ambient isotopic approximation.

We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections.

I argue that this construction makes sense for general constructible sheaves of categories on Kahler manifolds, without any symplectic interpretation of fibers.

We consider positive solutions to the semilinear heat equation wt= Δw+awlogw, a≠0, on complete Riemannian manifolds without boundary.

We also establish two integral criteria for rigidity that improve upon known, pointwise conditions, and hold for general manifolds without positivity conditions on the curvature.