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| 2. |
- Tkachev, Vladimir
(författare)
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Finiteness of the number of ends of minimal submanifolds in Euclidean space
- 1994
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Ingår i: Manuscripta mathematica. - : Springer Berlin/Heidelberg. - 0025-2611 .- 1432-1785. ; 82, s. 313-330
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Tidskriftsartikel (refereegranskat)abstract
- We prove a version of the well-known Denjoy-Ahlfors theorem about the number of asymptotic values of an entire function for properly immersed minimal surfaces of arbitrary codimension in ℝN. The finiteness of the number of ends is proved for minimal submanifolds with finite projective volume. We show, as a corollary, that a minimal surface of codimensionn meeting anyn-plane passing through the origin in at mostk points has no morec(n, N)k ends.
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| 3. |
- Tkachev, Vladimir
(författare)
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Some estimates for the mean curvature of graphs over domains in $R^n$
- 1991
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Ingår i: Doklady. Mathematics. - : Springer Berlin/Heidelberg. - 1064-5624 .- 1531-8362. ; 42:2, s. 387-390
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Tidskriftsartikel (refereegranskat)abstract
- Let f be a C2-solution in a domain Ω⊂Rn of the equationwhere H is a nondecreasing function of a real variable. In the particular case H(t)=a+bt, b>0, the preceding differential equation describes the capillarity in a tube of liquid [cf. R. Finn, Z. Angew. Math. Mech. 61 (1981), no. 3, 165–173; MR0626020]. The author establishes that ∫P|H[f(x)]|pdx≤cap(P,∂Ω;Ω), where ∂Ω is the boundary of Ω and cap(P,∂Ω,Ω) is the conformal capacity of a condenser (P,∂Ω;Ω) [cf., e.g., Yu. G. Reshetnyak, Spatial mappings with bounded distortion (Russian), see p. 52, "Nauka'' Sibirsk. Otdel., Novosibirsk, 1982; MR0665590]. The author also obtains estimates of the form supx∈Ω{|H[f(x)]|⋅dist(x,∂Ω)}≤p/n (1≤p≤n) for some categories of domains.
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| 4. |
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| 5. |
- Gudmundsson, Sigmundur, et al.
(författare)
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A note on the classification of holomorphic harmonic morphisms
- 1993
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Ingår i: Potential Analysis. - 1572-929X. ; 2:3, s. 295-298
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Tidskriftsartikel (refereegranskat)abstract
- In this note we give a complete classification of those holomorphic maps phgr:UrarrCopf n defined on open and connected subsets of Copf m which are harmonic morphisms.
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| 6. |
- Gudmundsson, Sigmundur
(författare)
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Harmonic morphisms between spaces of constant curvature
- 1993
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Ingår i: Proceedings of the Edinburgh Mathematical Society. - 1464-3839. ; 36, s. 133-143
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Tidskriftsartikel (refereegranskat)abstract
- Let M and N be simply connected space forms, and U an open and connected subset of M. Further let n: U-*N be a horizontally homothetic harmonic morphism. In this paper we show that if n has totally geodesic fibres and integrable horizontal distribution, then the horizontal foliation of U is totally umbilic and isoparametric. This leads to a classification of such maps. We also show that horizontally homothetic harmonic morphisms of codimension one are either Riemannian submersions modulo a constant, or up to isometries of M and N one of six well known examples.
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| 7. |
- Gudmundsson, Sigmundur
(författare)
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Harmonic morphisms from complex projective spaces
- 1994
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Ingår i: Geometriae Dedicata. - 0046-5755. ; 53:2, s. 155-161
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study harmonic morphisms emptyv :U sub CopfP m rarrN 2 from open subsets of complex projective spaces to Riemann surfaces. We construct many new examples of such maps which are not holomorphic with respect to the standard Kähler structure on CopfP m.
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| 8. |
- Gudmundsson, Sigmundur, et al.
(författare)
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Multivalued harmonic morphisms
- 1993
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Ingår i: Mathematica Scandinavica. - 0025-5521. ; 73, s. 127-155
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Tidskriftsartikel (refereegranskat)
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| 9. |
- Gudmundsson, Sigmundur
(författare)
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Non-holomorphic harmonic morphisms from Kähler manifolds
- 1994
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Ingår i: Manuscripta Mathematica. - 1432-1785. ; 85:1, s. 67-78
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Tidskriftsartikel (refereegranskat)abstract
- We give a method for constructing non-holomorphic harmonic morphisms from Kähler manifolds. The method is then used to obtain many such examples defined locally on the complex Grassmannians.
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| 10. |
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