Volume Growth of Shrinking Gradient Ricci-Harmonic Soliton
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DOI: 10.1007/s00025-017-0703-7
Abstract: In this paper, we study the shrinking gradient Ricci-harmonic soliton. Firstly using Chow–Lu–Yang’s argument, we give a necessary and sufficient condition for complete noncompact shrinking gradient Ricci-harmonic solitons with $$S\ge \delta $$S≥δ to have polynomial… read more here.
Keywords: gradient ricci; ricci harmonic; volume growth; harmonic soliton ... See more keywords
Rigid Properties of Generalized $$\tau $$-Quasi Ricci-Harmonic Metrics
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DOI: 10.1007/s00025-020-01299-w
Abstract: In this paper, we study compact generalized $$\tau $$ -quasi Ricci-harmonic metrics. In the first part, we explore conditions under which generalized $$\tau $$ -quasi Ricci-harmonic metrics are harmonic-Einstein and give some characterization results for… read more here.
Keywords: quasi ricci; harmonic metrics; tau quasi; ricci harmonic ... See more keywords
On f-non-parabolic ends for Ricci-harmonic metrics
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DOI: 10.1007/s10455-016-9525-1
Abstract: In this paper, we study gradient Ricci-harmonic soliton metrics and quasi Ricci-harmonic metrics (both metrics are called Ricci-harmonic). First, we prove that all ends of $$\tau $$τ-quasi Ricci-harmonic metrics with $$\tau >1$$τ>1 should be f-non-parabolic… read more here.
Keywords: quasi ricci; harmonic metrics; parabolic ends; ricci harmonic ... See more keywords
Monotonicity formulas for the first eigenvalue of the weighted p-Laplacian under the Ricci-harmonic flow
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DOI: 10.1186/s13660-019-1961-6
Abstract: Let Δp,ϕ$\Delta _{p,\phi }$ be the weighted p-Laplacian defined on a smooth metric measure space. We study the evolution and monotonicity formulas for the first eigenvalue, λ1=λ(Δp,ϕ)$\lambda _{1}=\lambda (\Delta _{p,\phi })$, of Δp,ϕ$\Delta _{p,\phi }$… read more here.
Keywords: weighted laplacian; first eigenvalue; formulas first; monotonicity formulas ... See more keywords
On the spectrum of the weighted p-Laplacian under the Ricci-harmonic flow
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DOI: 10.1186/s13660-020-02322-y
Abstract: This paper studies the behaviour of the spectrum of the weighted p-Laplacian on a complete Riemannian manifold evolving by the Ricci-harmonic flow. Precisely, the first eigenvalue diverges in a finite time along this flow. It… read more here.
Keywords: harmonic flow; spectrum weighted; weighted laplacian; ricci harmonic ... See more keywords