---
res:
  bibo_abstract:
  - In calculus, l'Hopital's rule provides a simple way to evaluate the limits of
    quotient functions when both the numerator and denominator vanish. But what happens
    when we move beyond real functions on a real interval? In this article, we study
    when the quotient of two complex-valued functions in higher dimension can be defined
    continuously at the points where both functions vanish. Surprisingly, the answer
    is far subtler than in the real-valued setting. We provide a complete characterization
    for the continuity of the quotient function. We also point out why extending this
    result to smoother quotients remains an intriguing challenge.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Albert
      foaf_name: Chern, Albert
      foaf_surname: Chern
  - foaf_Person:
      foaf_givenName: Sadashige
      foaf_name: Ishida, Sadashige
      foaf_surname: Ishida
      foaf_workInfoHomepage: http://www.librecat.org/personId=6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
    orcid: 0000-0002-3121-3100
  bibo_doi: 10.48550/ARXIV.2602.09958
  dct_date: 2026^xs_gYear
  dct_language: eng
  dct_subject:
  - l’Hopital theorem
  - complex functions
  dct_title: L'Hopital rules for complex-valued functions in higher dimensions@
...