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- JÃ©rÃ´me Bolte, Aris Daniilidis, Adrian S. Lewis, Masahiro Shiota
- SIAM Journal on Optimization
- 2007

We establish the following result: if the graph of a lower semicontinuous real-extendedvalued function f : Rn â†’ R âˆª {+âˆž} admits a Whitney stratification (so in particular if f is a semialgebraicâ€¦ (More)

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notionâ€¦ (More)

- F. Acquistapace, Fabrizio Broglia, Masahiro Shiota
- 2003

We prove a Lojasiewicz inequality for global semianalytic sets that implies the usual HÃ¶rmanderâ€™s form. Some consequences are deduced on the finiteness property and separation for global semianalyticâ€¦ (More)

- Goulwen Fichou, Masahiro Shiota
- 2017

We study the analytic equivalence of real analytic function germs after desingularization and state the cardinality of the classes under this equivalence relation. We consider also the Nash case, andâ€¦ (More)

This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazurâ€¦ (More)

We establish the following result: if the graph of a (nonsmooth) real-extended-valued function f : R n â†’ R âˆª {+âˆž} is closed and admits a Whitney stratification, then the norm of the gradient of f atâ€¦ (More)

More than half a century ago R. Thom asserted in an unpublished manuscript that, generically, vector fields on compact connected smooth manifolds without boundary can admit only trivial continuousâ€¦ (More)

- Goulwen Fichou, Masahiro Shiota
- 2017

The Euler characteristic of the link of a real algebraic variety is an interesting topological invariant in order to discuss local topological properties. We prove in the paper that an invariantâ€¦ (More)

- Goulwen Fichou, Masahiro Shiota
- 2008

By Hironaka Desingularization Theorem, any real analytic function has only normal crossing singularities after a modification. We focus on the analytic equivalence of such functions with only normalâ€¦ (More)

Approximation of real analytic functions by Nash functions is a classical topic in real geometry. In this paper, we focus on the Nash approximation of an analytic desingularization of a Nash functionâ€¦ (More)