Đánh giác các phép biến hình á bảo giác những miền nội tiếp trong hình vành khăn

tr 18-19]. Trongtrucmgh9'PcacbienngmiivabientrongcuamiSng6cvamiSnanhlacac ducmgironchungtoitimduqcc~ duaicuaq (xemcach~qua6 chuang6). 4.2 Banb gia M(r,f), m(r,f) BinbIf 4.2. V6i cackyhi~utrongchuang2,r labankinhduOngtrimtam0 nfuntrongmien E saochoQ <r <1, 'VfEF taco m(r,f)<~r~ (<rk), (4.3) M(r,f)~ t(~i[~q(~il (4.4) , ~-l, , Cacdangthucxayrafez)=aI z IK z+b, v6icachangsoa,bthichhqp ChUngminh:XemThu~n[19,21-22] BinbIf 4.3. V6i cackyhi~utrongchuang2,Vf E F vaVr:Q<r<l,taco M (r,f)::;; U <... <Uj < Uj-l <...UI<1, (4.5) m(r,f) 2::V >."Vj>Vj-l>...>VI>q, (4.6) Trongdo: 29 - I ) q J '=T ( p,rK,q , VI = [ ( Q ) ~- Ul T p, -; ,q (4.5a) - Uj=T (p,r~'Vj-l}Vj= [ , ( Qq ) t'~ J ' T P r UJ-I (4.6a) u =u ( K,p,Q,r,q )= l.im Uj'J~ <t) v =V (K ,P,Q ,r, q) =~imVj J~ 00 T(p,r,s)lahamph\!dinhnghiatrongchuong2. Chlmgminh:XemThao[14,tr.65]ho~cThu~n[19,tr22-25]. H~qua 4.1. Tir dinhly 4.3vatinhchfitcuahamT(p,r,s) trong(2.8)va(2.18)tadllilhgia dongianchoM(r,f) vam(r,f)nhusan: M(r,f)<T(p,r~,qJ <T(p,r~,0J <4~r~, (4.7) m(rf» q > q >~ , T[P'(~)~,qJ T[P'(~)~,oJ 4~(~r (4.8) 30 - 4 1 d - QK1~-=-<2P- C q . (4.13) 4.4 Daubgia If(z)1 Vi m(lzl,f)~lf(z)I~M(lzl,f) 'VzEE,nen'VfEFtac6: - q T[P'(I~I)k,qJ ~lf(Z)I~T(P,1Zlk,q}<1), (4.14) TirtinhchfttcuahamT(p,r,s)trong(2.8)va(2.18)tacodanhgiadongifmhon choIf(z)l: - q T[P{I;lto)<If(z)1<T(P,Izlk,o]. (4.15) 1 4~lq(I~I)K<[f(z)1<4~lzlt (4.16) 4.5 Daubgiacaedi~uticb V6i caeIcyhi~ua chuong2tacodanhgiacaedi~ntichcuami~ncinhB thong quaphepbiSnhinhf EF nhusau: - 2 ( 2 pS~SRK- - R ) K 2 Sl- Q , (4.17) 32 S(B)~S,[l-Rf}~[(~)f-1 (4.18) 2 sl~S(r,f)~S2rK, (4.19) m6i dtlngthucxily ra f(z)=aIz IK-Iz,lal=1. Chtmgminh:Xem[14,tr.58-59]ho~c[19,tr 19-20]. - - 4.6 Caedaubgiakhaeebocvad. Vi C ~ d~M(R,f),f E F nentiT(4.7)tacoc~trencuac,ngoairatrongtwang hgpbientrongcuamiSnB laduangtrim,tatill c~trenkhachoc nhugall: BiobIy4.5. V6i caekyhi~utrongchuang2 taco: ( - ) - nK R M ( q < c<qeV p~InQIn ~' f) (4.20) Chtmgminh: B~ngm9tphepquaythichhgpsaochomiSnE chuam9tcungtrimcod~ng LI ={zllzl=R,- ~~argz~~}. D~t EI ={zIQ<lzl<R,-~<argz<~}, BI =f(EI), BI c B(xemhinh4.2). 33 z EI .(QQ:~'-IR'. f E Hinh4.2v6'ip=2. Di[tt w =reiq>,ap dungb6 dS 2.9 cho PBHKABG tir £1 tenBI va l~y 1 1 B ' P=Iwl =~'WE 1ta co: S (B) 2~ 2fte p 1 K R PIn- Q Sp(B,) =Ifp2(w)ds=W~~<P:;;~If drd<p =211In M(~,f) 81 81 P q~lwl~M(R,f)r p q v6'i - C Idwl c Ip2f~=Inq'q Trong do ~ 27tlnM(~,f) 2~~ln2 ~ ~ln2 ~~7tKlnRln M(~,f) P q K InR q q p~ Q q Q 1tKInR InM(~,f) ~<qeV PP Q q , rnctaduQ'c(4.20). Chap4.1: 34 - 7tKIn!.1nM(!,f) NSu B =const,khi R~Q nghiala R ~1 thi qeVPJ3Q q ~ q <c, trong Q truemghgpnaydanhgiac~ trencuac larfitt61. Vi d~c~m(R,f),f EF, tir (4.8)tacoc~ du6'icuad. Ngoairatrpngtwemg hgpbienngoaicuami~nB laduemgtrimtadanhgia dnhusau: BlobIf 4.6 V6'icaeky hi~utrongchuang2 tadanhgia d nhusau: ( ,.., - ~,nK In 1 I 1 1 >)d>e V p~ m(R,f) oR (4.21) ChUngminh: BfuIgmQtphepquaythichhqpsaochomi~nE chuamQtclingtrimcod~g: LJ ={zllzl=R,-B~argz~B}. D~t E2={zIR<lzl<l,-B<argz<B}, B2=f(E2), B2cB(xem hinh4.3). (Q E2 z w 1f .. BE Hinh4.3v6'ip=2. f)~tw =reiq>, apd\mgb6d~2.9choPBHKABG ill £2lenB2val~yp =I~=~. Taco: S(B );:::~2fJe 2 KIP'In- R Sp(Bz)=ffp2(W)ds=ffr~~<P~!If drd<p=21tIn ! . 82 82 P m(R,f):=;JwI:=;Ir p m(R,f) v6i I >IfI dwI =In~, P-a Iwl d trong do =>2nIn 1 ~~~In2 ~ p m(R,f) K In~ d R 1tK 1 1 ( 1 J 2 =>-In In - ~ In-=- p~ m(R,f) R d 1 ~ In ~ < d nK I 1 I 1 n n- p~ m(R,f) R nK 1 1 - ,,{-In In- 'J p ~ m (R ,f) Rd >e ,tuctadugc4.21. 1tK 1 1 Chuy4.2n@u~=const,khi R~ 1thi e- ~pJ3Inm(R,f)InR ~ 1,trongtruangnay danhgiac~ du6icuad lar~t6t. 36 ._.