Geometric and differential properties of subanalytic sets

Bierstone, Edward; Milman, Pierre D.

doi:10.1090/S0273-0979-1991-16081-7

Geometric and differential properties of subanalytic sets

Authors: Edward Bierstone and Pierre D. Milman
Journal: Bull. Amer. Math. Soc. 25 (1991), 385-393
MSC (1985): Primary 32B20, 58C27; Secondary 32C42, 32K15
DOI: https://doi.org/10.1090/S0273-0979-1991-16081-7
MathSciNet review: 1102751
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1. Joseph Becker and William R. Zame, Applications of functional analysis to the solution of power series equations, Math. Ann. 243 (1979), no. 1, 37–54. MR 543093, https://doi.org/10.1007/BF01420205
2. Edward Bierstone and Pierre D. Milman, Composite differentiable functions, Ann. of Math. (2) 116 (1982), no. 3, 541–558. MR 678480, https://doi.org/10.2307/2007022
3. Edward Bierstone and Pierre D. Milman, The Newton diagram of an analytic morphism, and applications to differentiable functions, Bull. Amer. Math. Soc. (N.S.) 9 (1983), no. 3, 315–318. MR 714993, https://doi.org/10.1090/S0273-0979-1983-15190-X
4. E. Bierstone and P. D. Milman, Relations among analytic functions. I, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 1, 187–239 (English, with French summary). MR 894566
E. Bierstone and P. D. Milman, Relations among analytic functions. II, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 2, 49–77 (English, with French summary). MR 898931
5. Edward Bierstone and Pierre D. Milman, Local analytic invariants and splitting theorems in differential analysis, Israel J. Math. 60 (1987), no. 3, 257–280. MR 937792, https://doi.org/10.1007/BF02780394
6. Edward Bierstone and Pierre D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math. 67 (1988), 5–42. MR 972342
7. A. M. Gabrièlov, The formal relations between analytic functions, Funkcional. Anal. i Priložen. 5 (1971), no. 4, 64–65 (Russian). MR 0302930
8. A. M. Gabrièlov, Formal relations among analytic functions, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 1056–1090 (Russian). MR 0346184
9. Margherita Galbiati, Stratifications et ensemble de non-cohérence d’un espace analytique réel, Invent. Math. 34 (1976), no. 2, 113–128 (French). MR 0417443, https://doi.org/10.1007/BF01425478
10. Georges Glaeser, Fonctions composées différentiables, Ann. of Math. (2) 77 (1963), 193–209 (French). MR 0143058, https://doi.org/10.2307/1970204
11. Heisuke Hironaka, Local analytic dimensions of a subanalytic set, Proc. Japan Acad. Ser. A Math. Sci. 62 (1986), no. 2, 73–75. MR 839813
12. Shuzo Izumi, Gabrielov’s rank condition is equivalent to an inequality of reduced orders, Math. Ann. 276 (1986), no. 1, 81–89. MR 863708, https://doi.org/10.1007/BF01450926
13. Jean Merrien, Faisceaux analytiques semi-cohérents, Ann. Inst. Fourier (Grenoble) 30 (1980), no. 4, 165–219 (French). MR 599629
14. Pierre D. Milman, Analytic and polynomial homomorphisms of analytic rings, Math. Ann. 232 (1978), no. 3, 247–253. MR 0492359, https://doi.org/10.1007/BF01351429
15. W. Pawłucki, On relations among analytic functions and geometry of sub-analytic sets, Bull. Polish Acad. Sci. Math. 37 (1989), 117-125.