By applying a comparison theorem on trajectory-harps, we give an estimate of volumes of trajectory-balls for Kähler magnetic fields from below under an assumption that sectional curvatures of the underlying Kähler manifold are bounded from above.
"An estimate on volumes of trajectory-balls for Kähler magnetic fields." Proc. Japan Acad. Ser. A Math. Sci. 92 (4) 47 - 50, April 2016. https://doi.org/10.3792/pjaa.92.47