See Ahlfors theory on Wiktionary
{ "etymology_text": "Named after Finnish mathematician Lars Ahlfors (1907—1996), who published the theory in 1935.", "head_templates": [ { "args": { "1": "-" }, "expansion": "Ahlfors theory (uncountable)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Complex analysis", "orig": "en:Complex analysis", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Differential geometry", "orig": "en:Differential geometry", "parents": [ "Geometry", "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "ref": "1968, Joseph Belsley Miles, The Asymptotic Behavior of the Counting Function for the A-values of a Meromorphic Function, University of Wisconsin-Madison, page 29:", "text": "In this chapter we use Ahlfors' theory of covering surfaces to obtain results on the functional n(r,a).", "type": "quote" }, { "ref": "1986, Pacific Journal of Mathematics, volumes 122-123, page 441:", "text": "Terms of the form o(A(r)) in Ahlfors theory are given in the form cD(r) where c is a constant.", "type": "quote" }, { "ref": "2004, G. Barsegian, “A new program of investigations in analysis: Gamma-lines approaches”, in G. Barsegian, I. Laine, C. C. Yang, editors, Value Distribution Theory and Related Topics, Kluwer Academic, page 43:", "text": "The Ahlfors theory itself describes covering of curves or domains, but not covering of distinct, complex values #x5C;boldsymbol#x7B;a#x7D;.", "type": "quote" } ], "glosses": [ "A geometric counterpart to Nevanlinna theory that extends the applicability of the concept of covering surface (of a topological space) by defining a covering number (a generalised \"degree of covering\") applicable to any bordered Riemann surface equipped with a conformal Riemannian metric." ], "id": "en-Ahlfors_theory-en-noun-U~nYxt8g", "links": [ [ "complex analysis", "complex analysis" ], [ "differential geometry", "differential geometry" ], [ "Nevanlinna theory", "Nevanlinna theory" ], [ "covering surface", "covering space" ], [ "topological space", "topological space" ], [ "covering number", "covering number" ], [ "bordered Riemann surface", "bordered Riemann surface" ], [ "conformal", "conformal" ], [ "Riemannian metric", "Riemannian metric" ] ], "qualifier": "differential geometry", "raw_glosses": [ "(complex analysis, differential geometry) A geometric counterpart to Nevanlinna theory that extends the applicability of the concept of covering surface (of a topological space) by defining a covering number (a generalised \"degree of covering\") applicable to any bordered Riemann surface equipped with a conformal Riemannian metric." ], "synonyms": [ { "word": "Ahlfors' theory" }, { "word": "Ahlfors' theory of covering surfaces" } ], "tags": [ "uncountable" ], "topics": [ "complex-analysis", "mathematics", "sciences" ], "wikipedia": [ "Acta Mathematica", "Ahlfors theory", "Lars Ahlfors" ] } ], "word": "Ahlfors theory" }
{ "etymology_text": "Named after Finnish mathematician Lars Ahlfors (1907—1996), who published the theory in 1935.", "head_templates": [ { "args": { "1": "-" }, "expansion": "Ahlfors theory (uncountable)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "English entries with incorrect language header", "English eponyms", "English lemmas", "English multiword terms", "English nouns", "English terms with quotations", "English uncountable nouns", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "en:Complex analysis", "en:Differential geometry" ], "examples": [ { "ref": "1968, Joseph Belsley Miles, The Asymptotic Behavior of the Counting Function for the A-values of a Meromorphic Function, University of Wisconsin-Madison, page 29:", "text": "In this chapter we use Ahlfors' theory of covering surfaces to obtain results on the functional n(r,a).", "type": "quote" }, { "ref": "1986, Pacific Journal of Mathematics, volumes 122-123, page 441:", "text": "Terms of the form o(A(r)) in Ahlfors theory are given in the form cD(r) where c is a constant.", "type": "quote" }, { "ref": "2004, G. Barsegian, “A new program of investigations in analysis: Gamma-lines approaches”, in G. Barsegian, I. Laine, C. C. Yang, editors, Value Distribution Theory and Related Topics, Kluwer Academic, page 43:", "text": "The Ahlfors theory itself describes covering of curves or domains, but not covering of distinct, complex values #x5C;boldsymbol#x7B;a#x7D;.", "type": "quote" } ], "glosses": [ "A geometric counterpart to Nevanlinna theory that extends the applicability of the concept of covering surface (of a topological space) by defining a covering number (a generalised \"degree of covering\") applicable to any bordered Riemann surface equipped with a conformal Riemannian metric." ], "links": [ [ "complex analysis", "complex analysis" ], [ "differential geometry", "differential geometry" ], [ "Nevanlinna theory", "Nevanlinna theory" ], [ "covering surface", "covering space" ], [ "topological space", "topological space" ], [ "covering number", "covering number" ], [ "bordered Riemann surface", "bordered Riemann surface" ], [ "conformal", "conformal" ], [ "Riemannian metric", "Riemannian metric" ] ], "qualifier": "differential geometry", "raw_glosses": [ "(complex analysis, differential geometry) A geometric counterpart to Nevanlinna theory that extends the applicability of the concept of covering surface (of a topological space) by defining a covering number (a generalised \"degree of covering\") applicable to any bordered Riemann surface equipped with a conformal Riemannian metric." ], "tags": [ "uncountable" ], "topics": [ "complex-analysis", "mathematics", "sciences" ], "wikipedia": [ "Acta Mathematica", "Ahlfors theory", "Lars Ahlfors" ] } ], "synonyms": [ { "word": "Ahlfors' theory" }, { "word": "Ahlfors' theory of covering surfaces" } ], "word": "Ahlfors theory" }
Download raw JSONL data for Ahlfors theory meaning in All languages combined (2.9kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.