Asymptotics of Spectral Functions of Lower Energy Forms on Weakly 1-Complete Manifolds

Guokuan Shao; Wenxuan Wang; Xiquan Peng

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Asymptotics of Spectral Functions of Lower Energy Forms on Weakly 1-Complete Manifolds

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arxiv 2404.11908 v2 pith:OYWEKOVU submitted 2024-04-18 math.CV math.DG

Xiquan Peng , Guokuan Shao , Wenxuan Wang This is my paper · ORCID

classification math.CVmath.DG

keywords completeenergyformslowermanifoldmanifoldsweaklyasymptotics

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abstract

In this paper, we show that the optimal fundamental estimate holds true on a weakly $1$-complete manifold with mild conditions, then we establish the weak Morse inequalities for lower energy forms on the manifold. We also study the case for $q$-convex manifolds.

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