On the \(p\)-pseudoharmonic map heat flow. (English) Zbl 1457.32092
Summary: In this paper, we consider the heat flow for \(p\)-pseudoharmonic maps from a closed Sasakian manifold \((M^{2n+1},J,\theta)\) into a compact Riemannian manifold \((N^m,g_{ij})\). We prove global existence and asymptotic convergence of the solution for the \(p\)-pseudoharmonic map heat flow, provided that the sectional curvature of the target manifold \(N\) is non-positive. Moreover, without the curvature assumption on the target manifold, we obtain global existence and asymptotic convergence of the \(p\)-pseudoharmonic map heat flow as well when its initial \(p\)-energy is sufficiently small.
MSC:
| 32V05 | CR structures, CR operators, and generalizations |
| 32V20 | Analysis on CR manifolds |
| 53C56 | Other complex differential geometry |
Keywords:
\(p\)-pseudoharmonic map; \(p\)-pseudoharmonic map heat flow; Morse-type Harnack inequality; pseudohermitian manifold; Sasakian manifold; \(p\)-sublaplacianReferences:
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