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See detailSub-Laplacian comparison theorems on totally geodesic Riemannian foliations
Baudoin, Fabrice; Grong, Erlend; Kuwada, Kazumasa et al

in Calculus of Variations and Partial Differential Equations (2019), 58:130(4), 1-38

We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical ... [more ▼]

We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical Laplacians. In the case of Sasakian foliations, we show that sharp horizontal and vertical comparison theorems for the sub-Riemannian distance may be obtained as a limit of horizontal and vertical comparison theorems for the Riemannian distances approximations. [less ▲]

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See detailA priori estimates for Donaldson's equation over compact Hermitian manifolds
Li, Yi UL

in Calculus of Variations and Partial Differential Equations (2014), 50(3-4), 867-882

Detailed reference viewed: 105 (4 UL)