Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 2 min ago
PreprintCC BY 4.0arXiv

An exponential Lojasiewicz inequality for semi-Pfaffian sets

  • Nicolai Vorobjov
Open at sourcePDFDOICite

Abstract

We prove a generalization of the version, due to A. Gabrielov, of the Łojasiewicz inequality for not necessarily restricted semi-Pfaffian sets. Unlike the most variants of the Łojasiewicz inequality, it describes the rate of growth of a Pfaffian function on a semi-Pfaffian set X not only in a neighbourhood of its zero set in the domain of X but also in a neighbourhood of zeroes on the boundary of the domain. Gabrielov's version is essentially one-dimensional, we generalize it to a multidimensional case.

Related

  1. Exponential Lower Bounds for the Pfaffian Number of Graphs
    Priyanshu Pant, Ranveer Singh
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  2. Tubular Neighbourhoods of Pfaffian Sets and Applications to Neural Networks
    Paul Lezeau, Martin Lotz
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Hineva Inequality for Submanifolds of Real Space Forms with Semi-Symmetric Non-Metric Connection
    M. S. Lone, M. A. Lone
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Exponential Growth of Mean Multiplicities in Length Spectra of Semi-Arithmetic Surfaces of Arbitrary Arithmetic Dimension
    A. Zuevsky
    arXivPreprintCC0Full textAnalysis & PDEsarXiv
  5. Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality
    Guido De Philippis, Luca Gennaioli, Alessandro Pigati +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{vorobjov2026exponential,
  title = {{An exponential Lojasiewicz inequality for semi-Pfaffian sets}},
  author = {Nicolai Vorobjov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20361},
  eprint = {2609.20361},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20361},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An exponential Lojasiewicz inequality for semi-Pfaffian sets
AU  - Nicolai Vorobjov
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.20361
UR  - https://arxiv.org/abs/2609.20361
AB  - We prove a generalization of the version, due to A. Gabrielov, of the Łojasiewicz inequality for not necessarily restricted semi-Pfaffian sets. Unlike the most variants of the Łojasiewicz inequality, it describes the rate of growth of a Pfaffian function on a semi-Pfaffian set X not only in a neighbourhood of its zero set in the domain of X but also in a neighbourhood of zeroes on the boundary of the domain. Gabrielov's version is essentially one-dimensional, we generalize it to a multidimensional case.
ER  -