Complete manifolds with positive spectrum, II

By Peter Li, Jiaping Wang. 2001

180 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6113cb9cd770bf8929dfc315b4291d22dae99c36

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In Applied Mathematics

1. Jiaping Wang
2. Ovidiu Munteanu
3. G. Carron
4. Xiaodong Wang
5. F. Ledrappier
6. M. Rigoli
7. Peter Li
8. A. G. Setti

In Geometry and Topology

1. G. Carron
2. Jiaping Wang
3. Ovidiu Munteanu
4. Xiaodong Wang
5. F. Ledrappier
6. Peter Li
7. M. Rigoli
8. A. G. Setti

Citations in the corpus

• An integral formula for the volume entropy with applications to rigidity (2009, methodology): “t an equality. Therefore we have D2f = −(n−1) h g − 1 (n−1)2 df ⊗df i . From this one can show that N = R×Σn−1 with the metric g = dt2 +e2th, where h is a Riemannian metric on Σ. For more detail, cf. [LW3]. For anyp ∈ Σ let {ei}be anorthogonalbasis on(TpΣ,h). Bya simple calculation using the Gauss e”
• On the 1/H-flow by p-Laplace approximation: New estimates via fake distances under Ricci lower bounds (2019, background): “Wang, [60], suggests that this could be the case provided conditions (i) and (ii) in Example 3.”
• Weighted Poincaré inequality and rigidity of complete manifolds (2006, methodology): “This special case of Theorems A and B have been the subject of our earlier work [11,12].”
• Geometric inequalities for manifolds with Ricci curvature in the Kato class (2016, methodology): “. In the next section, we will review and collect some analytical tools that will be used in the paper, for instance we will describe some Agmon’s type volume estimate mainly due to P. Li and J.Wang ([33, 34]) that will be crucial for the proof of the Theorem A. We will also proved a new elliptic es”
• Smooth metric measure spaces with non-negative curvature (2011, background): “ess(f) = 0 and Mwould be Ricci flat. Historically, Cheng [10] proved a sharp upper bound of the bottom spectrum of the Laplacian on a complete manifold with Ricci curvature bounded below. Later on, in [20] and [21], P. Li and the second author studied the rigidity issue when the sharp upper bound is ”
• Geometry of manifolds with densities (2012, background): “s (1.2) hf (M) := limsup r→∞ lnVolf (Bp (r)) r . It is known if Ricf ≥ 0 and f has linear growth rate a, then (see [22]) hf (M) ≤ a. So our theorem deals with the case that hf (M) is maximal. Note by [2, 17] the following inequality holds true in general. (1.3) λ1 (∆f) ≤ 1 4 h2 f (M), where λ1 (∆f) ”