Geodesic
Problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 197-206

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The mathematical formulation of the problem on the propagation of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary is given for the principal term of the short-wave asymptotics, and the uniqueness of the solution of this problem is demonstrated. 
@article{ZNSL_1976_62_a15,
     author = {M. M. Popov},
     title = {Problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {197--206},
     publisher = {mathdoc},
     volume = {62},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a15/}
}
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M. M. Popov. Problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 197-206. http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a15/