V. GRADINARU AND R. HIPTMAIR † Abstract. Conforming finite elements inH(div; Ω) andH(curl; Ω) can be regarded as discrete differential forms (Whitney–forms). The construction of such forms is based on an interpolation idea, which boils down to a simple extension of the differential form to the interior of elements. This flexible approach can accommodate elements of more complicated shapes than ...

A canonically defined mod 2 linear dependency current is associated to each collection v of sections, Vl, . . . , Vm, of a real rank n vector bundle. This current is supported on the linear dependency set of v. It is defined whenever the collection v satisfies a weak measure theoretic condition called "atomicity." Essentially any reasonable collection of sections satisfies this condition, vastl...

In this paper, based on the classical Yano’s formula, we first establish an optimal integral inequality for compact Lagrangian submanifolds in complex space forms, which involves Ricci curvature direction \(J\mathbf {H}\) and norm of covariant differentiation second fundamental form h, where J is almost structure \(\mathbf mean vector field. Second analogously, Legendrian Sasakian forms with \(...