# Completeness and existence of bounded biharmonic functions on a riemannian manifold

Annales de l'institut Fourier (1974)

- Volume: 24, Issue: 1, page 311-317
- ISSN: 0373-0956

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topSario, Leo. "Completeness and existence of bounded biharmonic functions on a riemannian manifold." Annales de l'institut Fourier 24.1 (1974): 311-317. <http://eudml.org/doc/74166>.

@article{Sario1974,

abstract = {A.S. Galbraith has communicated to us the following intriguing problem: does the completeness of a manifold imply, or is it implied by, the emptiness of the class $H^2B$ of bounded nonharmonic biharmonic functions? Among all manifolds considered thus far in biharmonic classification theory (cf. Bibliography), those that are complete fail to carry $H^2B$-functions, and one might suspect that this is always the case. We shall show, however, that there do exist complete manifolds of any dimension that carry $H^2B$-functions. Moreover, there exist both complete and incomplete manifolds not permitting these functions, and, trivially, incomplete manifolds possessing them.},

author = {Sario, Leo},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {1},

pages = {311-317},

publisher = {Association des Annales de l'Institut Fourier},

title = {Completeness and existence of bounded biharmonic functions on a riemannian manifold},

url = {http://eudml.org/doc/74166},

volume = {24},

year = {1974},

}

TY - JOUR

AU - Sario, Leo

TI - Completeness and existence of bounded biharmonic functions on a riemannian manifold

JO - Annales de l'institut Fourier

PY - 1974

PB - Association des Annales de l'Institut Fourier

VL - 24

IS - 1

SP - 311

EP - 317

AB - A.S. Galbraith has communicated to us the following intriguing problem: does the completeness of a manifold imply, or is it implied by, the emptiness of the class $H^2B$ of bounded nonharmonic biharmonic functions? Among all manifolds considered thus far in biharmonic classification theory (cf. Bibliography), those that are complete fail to carry $H^2B$-functions, and one might suspect that this is always the case. We shall show, however, that there do exist complete manifolds of any dimension that carry $H^2B$-functions. Moreover, there exist both complete and incomplete manifolds not permitting these functions, and, trivially, incomplete manifolds possessing them.

LA - eng

UR - http://eudml.org/doc/74166

ER -

## References

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