"Ahlfors theory" meaning in English

{
  "etymology_text": "Named after Finnish mathematician Lars Ahlfors (1907—1996), who published the theory in 1935.",
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      "expansion": "Ahlfors theory (uncountable)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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          "kind": "topical",
          "langcode": "en",
          "name": "Complex analysis",
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          "kind": "topical",
          "langcode": "en",
          "name": "Differential geometry",
          "orig": "en:Differential geometry",
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            "Geometry",
            "Mathematical analysis",
            "Mathematics",
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            "Sciences",
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      "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": "quotation"
        },
        {
          "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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."
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          "complex analysis",
          "complex analysis"
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        [
          "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.",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        "en:Complex analysis",
        "en:Differential geometry"
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      "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": "quotation"
        },
        {
          "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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": [
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          "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"
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      "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"
}