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References
Bol, G., Über Nabelpunkte auf Eifläche.Math. Zeit., 49 (1944).
Gantmacher, F. R.,Applications of the Theory of Matrices. Interscience, New York (1959).
Hamburger, H., Beweis einer Caratheodoryschen Vermutung I.Ann. of Math., 2 (1940), 63–86.
Hamburger, H., Beweis einer Caratheodoryschen Vermutung II, III.Acta Math., (1941), 175–228, 229–332.
Klotz, T., On G. Bol's Proof of the Caratheodory Conjecture.Comm. Pure Appl. Math., 12 (1959), 277–311.
Lefschetz, S.,Differential Equations, Geometric Theory. Interscience, New York, 2nd Edition.
Little, J. A., Geometric Singularities.Proc. Liverpool Singularities Symposium II, Lecture Notes, 209, Springer, 1971, 118–120.
Loewner, C., A Topological Characterization of a Class of Integral Operators.Ann. of Math., 41 (1940) 63–86.
Milnor, J. W.,Topology from the Differentiable Viewpoint. Univ. of Virginia Press, Charlottesville, 1965.
Semple, J. G. & Kneebone, G. T.,Algebraic Curves. Oxford, 1959.
Titus, C. J., The Combinatorial Topology of Analytic Functions on the Boundary of a Disc.Acta Math., 106 (1961), 45–64.
Titus, C. J.,Transformation Semigroups and Extensions to Sensepreserving Mappings. Aarhus Univ. Math. Inst. Preprint Ser. 1970/71, No. 35.
—, Characterizations of the Restriction of a Holomorphic Function to the Boundary of a Disc.J. d'Analyse, 18 (1957), 351–358.
Titus, C. J. &Young, G. S., An Extension Theorem for a Class of Differential Operators.Mich. Math. J., 6 (1959), 195–204.
Wall, C. T. C., Remark on Geometric Singularities.Proc. Liverpool Singularities Symposium II, Lecture Notes, 209, Springer, 1971, 121.
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Titus, C.J. A proof of a conjecture of Loewner and of the conjecture of caratheodory on umbilic points. Acta Math. 131, 43–77 (1973). https://doi.org/10.1007/BF02392036
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DOI: https://doi.org/10.1007/BF02392036