Download A Course of Differential Geometry and Topology by Aleksandr Sergeevich Mishchenko PDF

By Aleksandr Sergeevich Mishchenko

This can be basically a textbook for a contemporary path on differential geometry and topology, that is a lot wider than the conventional classes on classical differential geometry, and it covers many branches of arithmetic a data of which has now develop into crucial for a latest mathematical schooling. we are hoping reader who has mastered this fabric could be capable of do self sufficient study either in geometry and in different comparable fields. to realize a deeper knowing of the fabric of this publication, we advise the reader should still remedy the questions in A.S. Mishchenko, Yu.P. Solovyev, and A.T. Fomenko, difficulties in Differential Geometry and Topology (Mir Publishers, Moscow, 1985) which was once especially compiled to accompany this path.

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Example text

BVP for Pluriholomorphic ... 1) by the transformation s=z- qz. 8) where (S) is a pluriholomorphic function. First BVP are solved for pluriholomorphic functions. Let D be the half plane y > 0. Problem 1. 1) that vanishes at infinity by the conditions akw I Rek ay y=o = A(x), k = 0,1, ... ,n-1. 9) Solution. 11) /CPk(Z), 0 where cpdz) are any holomorphic functions. Let n = 2. 9) we have Re CPo (x) = fo(x), Re [CPl (x) + icpb(x)] = II (x), By these conditions the holomorphic functions cpo(z) and CPl (z) as cpo(z) CPl (z) 1- - , 1II +- 1 1 = ---;:rrz 1 7r x E R.

1) in D and D-, w(oo) = O. 16) Let rl, r2, ... , r. rn be smooth lines situated inside the domain D with the boundary Problem 1. 16). Note that this problem is investigated in the sense of solvability for a variable B [Vel. 15). Problem 2. (t), t E R(-oo, 00), where f(t) is a given HOlder-continuous function. 17) 30 I. Two-Dimensional Cases Solution. 1). Let L be a straight line ax +,8y = 0. Without loss of generality one can assume a 2+,82 = 1. The symmetric points with respect to L are z and z* = -(a + i,8)2 Z.

22), one can write these two conditions as a system of Hilbert BVP for <1>1 and cI>2 + M(t)]i(t) + mM(t)l(t) = 2"(t) +g+ (t) , [1 + M( -t)]<1>l (t) + mM( -t)i(t) = i(t) + g+( -t), [1 t E R.

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