No Access

ŁOJASIEWICZ INEQUALITY FOR POLYNOMIAL FUNCTIONS ON NON-COMPACT DOMAINS

DINH SI TIEP

Institute of Mathematics, 18 Hoang Quoc Viet Road, Cau Giay District, 10307, Hanoi, Vietnam

Search for more papers by this author

HA HUY VUI

Institute of Mathematics, 18 Hoang Quoc Viet Road, Cau Giay District, 10307, Hanoi, Vietnam

Search for more papers by this author

, and

NGUYEN THI THAO

Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Road, Cau Giay District, Hanoi, Vietnam

Search for more papers by this author

https://doi.org/10.1142/S0129167X12500334Cited by:11 (Source: Crossref)

Abstract

In this paper we give some versions of the Łojasiewicz inequality on non-compact domains for polynomial functions. We also point out some relations between the existence Łojasiewicz inequality and the phenomenon of singularities at infinity.

Keywords:

References

S. Basu , R. Pollack and M. Roy , Algorithms in Real Algebraic Geometry , Algorithms and Computation in Mathematics 10 ( Springer , 2003 ) . Crossref, Google Scholar
R. Benedetti and J. Risler , Real Algebraic and Semi-Algebraic Sets ( Hermann , 1991 ) . Google Scholar
J. Bochnak , M. Coste and M.-F. Roy , Real Algebraic Geometry 36 ( Springer , 1998 ) . Crossref, Google Scholar
M. Coste and M. J. de la Puente, J. Pure Appl. Algebra 162(1), 23 (2001), DOI: 10.1016/S0022-4049(00)00111-0. Crossref, Web of Science, Google Scholar
I. Ekeland, Bull. Amer. Math. Soc. 1, 443 (1979), DOI: 10.1090/S0273-0979-1979-14595-6. Crossref, Web of Science, Google Scholar
Hörmander, Ark. Mat. 3, 555 (1958), DOI: 10.1007/BF02589517. Crossref, Google Scholar
S. Ji, J. Kollar and B. Shiffman, Trans. Amer. Math. Soc. 329(2), 813 (1992), DOI: 10.2307/2153965. Web of Science, Google Scholar
S. Łojasiewicz, Studia Math. 18, 87 (1959). Crossref, Google Scholar
S. Łojasiewicz , Ensembles Semi-Analytiques ( Institutdes Hautes Etudes Scientifiques , Bures-sur-Yvette , 1965 ) . Google Scholar
Z.-Q. Luo and J. F. Sturm, High Performance Optimization, Applied Optimization (Kluwer Academic Publishers, Dordrecht, 2000) pp. 383–404. Crossref, Google Scholar
R. Thom, Bull. Amer. Math. Soc. 75, 249 (1969), DOI: 10.1090/S0002-9904-1969-12138-5. Google Scholar
M. Tibar and A. Zaharia, Manuscripta Math. 99, 383 (1999). Web of Science, Google Scholar
H. H. Vui and N. H. Duc, Math. Z 266, 243 (2010), DOI: 10.1007/s00209-009-0567-y. Crossref, Web of Science, Google Scholar
Y. Yomdin and G. Comte , Tame Geometry with Application in Smooth Analysis , Lecture notes in Mathematics 1834 ( Springer , 2004 ) . Crossref, Google Scholar