# The fixed points of holomorphic maps on a convex domain

Annales Polonici Mathematici (1992)

- Volume: 56, Issue: 2, page 143-148
- ISSN: 0066-2216

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topDo Duc Thai. "The fixed points of holomorphic maps on a convex domain." Annales Polonici Mathematici 56.2 (1992): 143-148. <http://eudml.org/doc/262465>.

@article{DoDucThai1992,

abstract = {We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in $ℂ^n$ then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.},

author = {Do Duc Thai},

journal = {Annales Polonici Mathematici},

keywords = {fixed points; holomorphic maps; convex domains},

language = {eng},

number = {2},

pages = {143-148},

title = {The fixed points of holomorphic maps on a convex domain},

url = {http://eudml.org/doc/262465},

volume = {56},

year = {1992},

}

TY - JOUR

AU - Do Duc Thai

TI - The fixed points of holomorphic maps on a convex domain

JO - Annales Polonici Mathematici

PY - 1992

VL - 56

IS - 2

SP - 143

EP - 148

AB - We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in $ℂ^n$ then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.

LA - eng

KW - fixed points; holomorphic maps; convex domains

UR - http://eudml.org/doc/262465

ER -

## References

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- [11] L. Lempert, Holomorphic retracts and intrinsic metrics in convex domains, Anal. Math. 8 (1982), 257-261. Zbl0509.32015
- [12] H. L. Royden and P. Wong, Carathéodory and Kobayashi metrics on convex domains, to appear.
- [13] E. Vesentini, Complex geodesics, Compositio Math. 44 (1981), 375-394. Zbl0488.30015
- [14] E. Vesentini, Complex geodesics and holomorphic maps, in: Sympos. Math. 26, Inst. Naz. Alta Mat. Fr. Severi, 1982, 211-230. Zbl0506.32008
- [15] J.-P. Vigué, Points fixes d’applications holomorphes dans un domaine borné convexe de ${\u2102}^{n}$, Trans. Amer. Math. Soc. 289 (1985), 345-353. Zbl0589.32043

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