Exponentially Harmonic Maps, Gauss Maps and Gauss Sections
Sign Up to like & getrecommendations! Published in 2019 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-019-1408-9
Abstract: We investigate the relationship of Ricci form, exponential tension field and tension field of the Gauss map of an immersion from a Riemannian manifold into a Riemannian space form. We also study exponentially harmonic Gauss… read more here.
Keywords: maps gauss; gauss sections; harmonic maps; exponentially harmonic ... See more keywords
Some Remarks on Bi-f-Harmonic Maps and f-Biharmonic Maps
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DOI: 10.1007/s00025-019-1023-x
Abstract: In this paper, we prove that the class of bi-f-harmonic maps and that of f-biharmonic maps from a conformal manifold of dimension $$\ge 3$$≥3 are the same (Theorem 1.1). We also give several results on… read more here.
Keywords: harmonic maps; biharmonic maps; maps biharmonic; remarks harmonic ... See more keywords
On the Evolution of Regularized Dirac-Harmonic Maps from Closed Surfaces
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DOI: 10.1007/s00025-020-1178-5
Abstract: We study the evolution equations for a regularized version of Dirac-harmonic maps from closed Riemannian surfaces. We establish the existence of a global weak solution for the regularized problem, which is smooth away from finitely… read more here.
Keywords: harmonic maps; evolution; maps closed; dirac harmonic ... See more keywords
A Note on the uncoupled Dirac-harmonic maps from Kähler spin manifolds to Kähler manifolds
Sign Up to like & getrecommendations! Published in 2018 at "manuscripta mathematica"
DOI: 10.1007/s00229-017-0941-8
Abstract: In this manuscript, we consider uncoupled Dirac-harmonic maps from Kähler spin manifolds to Kähler manifolds and prove an existence theorem. Moreover, we construct some new uncoupled Dirac-harmonic maps from Riemann surfaces to Kähler manifolds. read more here.
Keywords: hler; dirac harmonic; harmonic maps; hler manifolds ... See more keywords
Exponentially harmonic maps between Finsler manifolds
Sign Up to like & getrecommendations! Published in 2018 at "manuscripta mathematica"
DOI: 10.1007/s00229-017-0981-0
Abstract: Exponentially harmonic maps and harmonic maps are different. In this paper, we derive the first and second variations of the exponential energy of a smooth map between Finsler manifolds. We show that a non-constant exponentially… read more here.
Keywords: exponentially harmonic; finsler manifolds; harmonic maps; maps finsler ... See more keywords
Equivariant harmonic maps depend real analytically on the representation
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DOI: 10.1007/s00229-021-01345-z
Abstract: We consider harmonic maps into symmetric spaces of non-compact type that are equivariant for representations that induce a free and proper action on the symmetric space. We show that under suitable non-degeneracy conditions such equivariant… read more here.
Keywords: real analytically; equivariant harmonic; depend real; harmonic maps ... See more keywords
Families of spherical surfaces and harmonic maps
Sign Up to like & getrecommendations! Published in 2017 at "Geometriae Dedicata"
DOI: 10.1007/s10711-018-0389-3
Abstract: We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifurcations explicitly using loop group methods. Constant Gaussian curvature surfaces… read more here.
Keywords: harmonic maps; surfaces harmonic; families spherical; spherical surfaces ... See more keywords
Exponentially harmonic maps between surfaces
Sign Up to like & getrecommendations! Published in 2018 at "Analysis and Mathematical Physics"
DOI: 10.1007/s13324-018-0270-4
Abstract: We show the maximum principle for exponential energy minimizing maps. We then estimate the distance of two image points of an exponentially harmonic map between surfaces. We also study the existence of an exponentially harmonic… read more here.
Keywords: exponentially harmonic; harmonic maps; maps surfaces; harmonic map ... See more keywords
Fractional div-curl quantities and applications to nonlocal geometric equations
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DOI: 10.1016/j.jfa.2018.03.016
Abstract: Abstract We investigate a fractional notion of gradient and divergence operator. We generalize the div-curl estimate by Coifman–Lions–Meyer–Semmes to fractional div-curl quantities, obtaining, in particular, a nonlocal version of Wente's lemma. We demonstrate how these… read more here.
Keywords: harmonic maps; div curl; curl quantities; fractional div ... See more keywords
CR-HARMONIC MAPS
Sign Up to like & getrecommendations! Published in 2019 at "Nagoya Mathematical Journal"
DOI: 10.1017/nmj.2019.40
Abstract: We develop the notion of renormalized energy in Cauchy–Riemann (CR) geometry for maps from a strictly pseudoconvex pseudo-Hermitian manifold to a Riemannian manifold. This energy is a CR invariant functional whose critical points, which we… read more here.
Keywords: harmonic maps; geometry;
Schwarz Pick type inequalities for harmonic maps between Riemann surfaces
Sign Up to like & getrecommendations! Published in 2018 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2018.1530664
Abstract: ABSTRACT We study the Schwarz lemma for harmonic mappings in general setting and prove among the other results that: if is the class of harmonic mappings f of the unit disk into the geodesic disk… read more here.
Keywords: schwarz pick; maps riemann; inequalities harmonic; harmonic maps ... See more keywords