Abstract
We present a topological classification of linearly convex domains with almost smooth boundary whose singularities lie in a hyperplane. We investigate sets with linearly convex boundary and the closures of linearly convex domains.
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References
Yu. B. Zelinskii, “On linear convex domains with smooth boundaries,” Ukr. Mat. Zh., 40, No. 1, 53–58 (1988).
L. Ya. Makarova, “Sufficient conditions for the linear convexity of domains with almost smooth boundaries,” in: On Holomorphic Functions of Many Complex Variables [in Russian], Institute of Physics, Academy of Sciences of the USSR (Siberian Division), Krasnoyarsk (1976), pp. 87–96.
V. L. Mel’nik, “On linearly convex domains with smooth boundaries,” Ukr. Mat. Zk., 49, No. 11, 1153–1156 (1997).
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Mel’nik, V.L. Linearly convex domains with singularities on the boundary. Ukr Math J 52, 464–469 (2000). https://doi.org/10.1007/BF02513140
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DOI: https://doi.org/10.1007/BF02513140