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A SCHWARZ LEMMA FOR
$V$-HARMONIC MAPS AND THEIR APPLICATIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 96 / Issue 3 / December 2017
- Published online by Cambridge University Press:
- 17 August 2017, pp. 504-512
- Print publication:
- December 2017
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We establish a Schwarz lemma for
$V$-harmonic maps of generalised dilatation between Riemannian manifolds. We apply the result to obtain corresponding results for Weyl harmonic maps of generalised dilatation from conformal Weyl manifolds to Riemannian manifolds and holomorphic maps from almost Hermitian manifolds to quasi-Kähler and almost Kähler manifolds.
SOME REMARKS ON THE PIGOLA–RIGOLI–SETTI VERSION OF THE OMORI–YAU MAXIMUM PRINCIPLE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 89 / Issue 2 / April 2014
- Published online by Cambridge University Press:
- 19 August 2013, pp. 337-342
- Print publication:
- April 2014
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We prove that the hypotheses in the Pigola–Rigoli–Setti version of the Omori–Yau maximum principle are logically equivalent to the assumption that the manifold carries a
${C}^{2} $ proper function whose gradient and Hessian (Laplacian) are bounded. In particular, this result extends the scope of the original Omori–Yau principle, formulated in terms of lower bounds for curvature.
ON MINIMAL SURFACES SATISFYING THE OMORI–YAU PRINCIPLE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 84 / Issue 1 / August 2011
- Published online by Cambridge University Press:
- 16 June 2011, pp. 33-39
- Print publication:
- August 2011
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