Sentence examples for be a complete noncompact from inspiring English sources

Let (M,g) be a complete noncompact Riemannian n-manifold (n⩾2).

Let M be a complete noncompact Riemannian.

Theorem 1.2 Let ( M, F, d μ ) be a complete noncompact Finsler n-manifold with finite reversibility λ.

Theorem 1.3 Let ( M, F, d μ ) be a complete noncompact and simply connected Finsler n-manifold with finite reversibility λ and nonpositive S-curvature.

Theorem 5.2 Let ( M, F, d μ ) be a complete noncompact and simply connected Finsler n-manifold with finite reversibility λ, nonpositive flag curvature and nonpositive S-curvature.

Corollary 1.4 Let ( M, g ) be a complete noncompact n-dimensional Riemannian manifold with Ricci tensor bounded from below by the constant − K = : − K ( M ), where K > 0. Assume that u is a positive solution of (1.1) with u ≤ M 1 for all ( x, t ) ∈ M × ( 0, + ∞ ).

Since f is arbitrary, the formula above means λ 1 ( B p ( R ) ) ≥ [ ( n − 1 ) a coth ( a R ) 2 λ ] 2. Note that ( M, F, d μ ) is a complete noncompact and simply connected Finsler manifold.

Let M be a complete, connected noncompact manifold with bounded geometry.

"I'll be a complete voyeur".

It is an important problem to determine when a complete noncompact Riemannian manifold admits a positive Green's function.

Corollary 4.4 A complete noncompact Finsler n-manifold with nonnegative weighted Ricci curvature and finite reversibility must have infinite volume.