References of "Wang, Feng-Yu"
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See detailGradient Estimates on Dirichlet and Neumann Eigenfunctions
Arnaudon, Marc; Thalmaier, Anton UL; Wang, Feng-Yu

in International Mathematics Research Notices (in press)

By methods of stochastic analysis on Riemannian manifolds, we derive explicit two-sided gradient estimates for Dirichlet eigenfunctions on a d-dimensional compact Riemannian manifold D with boundary ... [more ▼]

By methods of stochastic analysis on Riemannian manifolds, we derive explicit two-sided gradient estimates for Dirichlet eigenfunctions on a d-dimensional compact Riemannian manifold D with boundary. Corresponding two-sided gradient estimates for Neumann eigenfunctions are derived in the second part of the paper. [less ▲]

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See detailEquivalent Harnack and gradient inequalities for pointwise curvature lower bound
Arnaudon, Marc; Thalmaier, Anton UL; Wang, Feng-Yu

in Bulletin des Sciences Mathématiques (2014), 138(5), 643-655

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See detailA stochastic approach to a priori estimates and Liouville theorems for harmonic maps
Thalmaier, Anton UL; Wang, Feng-Yu

in Bulletin des Sciences Mathématiques (2011), 135(6-7), 816-843

Nonlinear versions of Bismut type formulas for the differential of a harmonic map between Riemannian manifolds are used to establish a priori estimates for harmonic maps. A variety of Liouville type ... [more ▼]

Nonlinear versions of Bismut type formulas for the differential of a harmonic map between Riemannian manifolds are used to establish a priori estimates for harmonic maps. A variety of Liouville type theorems is shown to follow as corollaries from such estimates by exhausting the domain through an increasing sequence of geodesic balls. This probabilistic method is well suited for proving sharp estimates under various curvature conditions. We discuss Liouville theorems for harmonic maps under the following conditions: small image, sublinear growth, non-positively curved targets, generalized bounded dilatation, Liouville manifolds as domains, certain asymptotic behaviour. [less ▲]

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See detailGradient estimates and Harnack inequalities on non-compact Riemannian manifolds
Arnaudon, Marc; Thalmaier, Anton UL; Wang, Feng-Yu

in Stochastic Processes & Their Applications (2009), 119(10), 3653-3670

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See detailHarnack inequality and heat kernel estimates on manifolds with curvature unbounded below
Arnaudon, Marc; Thalmaier, Anton UL; Wang, Feng-Yu

in Bulletin des Sciences Mathématiques (2006), 130(3), 223-233

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See detailDerivative estimates of semigroups and Riesz transforms on vector bundles
Thalmaier, Anton UL; Wang, Feng-Yu

in Potential Analysis (2004), 20(2), 105-123

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See detailGradient estimates for harmonic functions on regular domains in Riemannian manifolds
Thalmaier, Anton UL; Wang, Feng-Yu

in Journal of Functional Analysis (1998), 155(1), 109-124

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