Convergence and quasi-optimality of adaptive finite element methods for harmonic forms
Sign Up to like & getrecommendations! Published in 2017 at "Numerische Mathematik"
DOI: 10.1007/s00211-016-0862-6
Abstract: Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework also relies extensively on accurate computation… read more here.
Keywords: finite element; adaptive finite; element methods; harmonic forms ... See more keywords
$$L^{2}$$L2 harmonic forms on complete special holonomy manifolds
Sign Up to like & getrecommendations! Published in 2019 at "Annals of Global Analysis and Geometry"
DOI: 10.1007/s10455-019-09654-z
Abstract: In this article, we consider $$L^{2}$$L2 harmonic forms on a complete non-compact Riemannian manifold X with a nonzero parallel form $$\omega $$ω. The main result is that if $$(X,\omega )$$(X,ω) is a complete $$G_{2}$$G2- (or… read more here.
Keywords: forms complete; harmonic forms; spin; complete special ... See more keywords
Harmonic forms on the Kodaira-Thurston manifold
Sign Up to like & getrecommendations! Published in 2022 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2022.108277
Abstract: We introduce an effective method to solve the $\bar\partial$-harmonic forms on the Kodaira-Thurston manifold endowed with an almost complex structure and an Hermitian metric. Using the Weil-Brezin transform, we reduce the elliptic PDE system to… read more here.
Keywords: harmonic forms; forms kodaira; thurston manifold; kodaira thurston ... See more keywords
VANISHING THEOREMS FOR HYPERSURFACES IN THE UNIT SPHERE
Sign Up to like & getrecommendations! Published in 2018 at "Glasgow Mathematical Journal"
DOI: 10.1017/s0017089517000350
Abstract: Abstract Let Mn, n ≥ 3, be a complete hypersurface in $\mathbb{S}$n+1. When Mn is compact, we show that Mn is a homology sphere if the squared norm of its traceless second fundamental form is… read more here.
Keywords: harmonic forms; vanishing theorems; hypersurfaces unit; theorems hypersurfaces ... See more keywords
Bott–Chern harmonic forms on complete Hermitian manifolds
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Mathematics"
DOI: 10.1142/s0129167x19500289
Abstract: Let [Formula: see text] be a Hermitian manifold of complex dimension [Formula: see text]. Assume that the torsion of the Chern connection [Formula: see text] is bounded, and that there exists a [Formula: see text]exhausting… read more here.
Keywords: harmonic forms; chern harmonic; formula see; see text ... See more keywords