  This paper is devoted to construction of finitely presented infinite nil
semigroup with identity $x^9=0$. This construction answers to the problem of
Lev Shevrin and Mark Sapir. The paper is quite long so the proof is separated
into geometric, combinatorial and finalization parts. In the first part we
construct uniformly elliptic space. Space is called {\it uniformly elliptic} if
any two points $A$ and $B$ at the distance of $D$ can be connected by the
system of geodesics which form a disc with width $\lambda\cdot D$ for some
global constant $\lambda>0$. In the second part we study combinatorial
properties of the constructed complex. Vertices and edges of this complex coded
by finite number of letters so we can consider semigroup of paths. Defining
relations correspond to pairs of equivalent short paths on the complex.
Shortest path in sense of natural metric correspond nonzero words in the
semigroup. Words which are not presented as paths on complex and words
correspond to non shortest paths can be reduced to zero. In the third part we
make a finalization. In particular, we show that word containing ninth degree
word can be reduced to zero by defining relations. The present paper contains
first part of the proof. This work was carried out with the help of the Russian
Science Foundation Grant N 17-11-01377. The first author is the winner of the
contest Young Mathematics of Russia .
