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H~Sh NgtQ!h ΞfQUO_ SN'Yf[QHr>y 1987. Yef[e_N^:N;N ~TT{u0 zSB020242 z Ty^~'`Rg ;` f[ e54 f[ R2 _f[g,{Nf[g _USMOpef[NOo`yf[f[b NYe^lR Q[iS_Npef[xvzvvW,g N/f^~'`v. Bl^~'`]~ gNNN͑vel. ,g zv;Nvv/fN~vQ-NNNel; ;NQ[ g: 1, BanachzztV~TvQ Nv_Rt. 2, Qpe[t. 3, R/etRek. 4, NRp[t. 5. Brouwer^t, 6, Leray-Schauder^t. 6. N N[tTt(WOP_Re z-Nv^(u. 7. SRt{N. YePgS;NSfN 1bNY HQN HeS ^~'`lQRg_ pQ]'Yf[QHr>y 2004. 2'Y ^~'`lQRg q\Nyf[b/gQHr>y 2004. 3, L. Nirenberg, Nonlinear Functional Analysis, Courant Lecture Notes Series, 1974. 4 _m`^; Methods of Nonlinear Analysis, Springer, 2005. Yef[e_N^:N;N ~TT{u0 zSB020243 z Ty{P[JSt ;` f[ e54 f[ R2 _f[g,{Nf[g _USMOpef[NOo`yf[f[b NYe^lR Q[i 1 gLu~'`{P[Sewz\ubCQ2 Cauchy3 ^~'`SU\e zI{0 YePgS;NSfN 1. A. Pazy, Semigroups of linear operators and applications to partial differential equations Springer-Verlag, 1983. Yef[e_N^:N;N ~TT{u0 zSB020232 z Ty;NN NvT~ ;` f[ e72 f[ R3 _f[g,{Nf[g _USMOpef[NOo`yf[f[b NYe^NgtQ!h Q[iTϑN NvT~T4ls^R^ hgNTT~ _R~~N ;N~~N NvT~ ;NN NT~vfs Yang-Mill:W YePgTSfNv 1. H~Sh NgtQ!hΞfQUO_ NQ SN'Yf[QHr>y 2004t^1g 2. ss^;NN Nv_RQUO SN'Yf[IN Yef[e_N^:N;N ~TT{u0 zSB020233 z TyNgNNgNpe ;` f[ e72 f[ R3 _f[g,{Nf[g _USMOpef[NOo`yf[f[b NYe^NgtQ!h Q[i: Ngvi_ NgTNgNpe NgTNgNpevh:y SL(2,C)vh:yTtbnfbe{P[ NgNpev~gt YJSUSNgNpe 9h| JSUSNgNpevh:y YePgTSfNv 1.%N_, N: LieSvQLieNpe ؚI{YeQHr>y 1985t^10g 2. K. J. Alexander, An Introduction to Lie Groups and Lie Algebras; 3. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory 4. S. Helgason, Differential Geometry, Lie groups, and Symmetric Spaces, Academic Press, Inc., 1978 Yef[e_N^:N;N ~TT{u0 zSB020245 z TyG-~gvQUO ;` f[ e54 f[ R2 _f[g,{Nf[g _USMOpef[NOo`yf[f[b NYe^NgtQ!h Q[iG-~gvi_ 8^vG-~gOP[ G-~gvQUO yrkTPN pef[irt-NvG-~g YePgTSfNv 1. S. S. Chern, The geometry of G-structures, Bull. Amer. Math. Soc. Volume 72, Number 2 (1966), 167-219; 2. D. V. Alekseevsky , Peter W. Michor, Differential Geometry of G-Manifolds Yef[e_N^:N;N ~TT{u0 zSB020246 z Ty[yzz ;` f[ e54 f[ R2 _f[g,{Nf[g _USMOpef[NOo`yf[f[b NYe^NgtQ!h Q[iΞf[yzzvi_ Ξf[y[ Ξf[yzzvOP[ ckN[yNgNpe Ξf[yzzvfs _ϑ YePgTSfNv 1. H~Sh NgtQ!hΞfQUO_ NQ SN'Yf[QHr>y 2004t^1g; 2. S. Helgason, Differential Geometry, Lie groups, and Symmetric Spaces, Academic Press, Inc., 1978 Yef[e_N^:N;N ~TT{u0 zSB020247 z TyQUORgRek ;` f[ e54 f[ R2 _f[g,{Nf[g _USMOpef[NOo`yf[f[b NYe^lR Q[i(1) First and Second Variational Formulas for Area(2) Bishop Comparison Theorem(3) Bochner-Weitzenbock Formulas(4) Laplacian Comparison Theorem(5) Poincare Inequality and the First Eigenvalue(6) Gradient Estimate and Harnack Inequality(7) Mean Value Inequality(8) Reilly's Formula and Applications(9) Isoperimetric Inequalities and Sobolev Inequalities(10) Lower Bounds of Isoperimetric Inequalities(11) Harnack Inequality and Regularity Theory of De Giorgi-Nash-Moser YePgTSfNv 1.P. Li, Lectures on geometric analysis, UCI lecture note, 2009. 2. T. Aubin, Some problems in Riemannian Geometry, Springer. eEQf: :Nf[ucO5uP[HrINTSfN. Yef[e_N^:N;N ~TT{u0 zSB020248 z TyQUORg-NvRicciAmt ;` f[ e54 f[ R2 _f[g,{Nf[g _USMOpef[NOo`yf[f[b NYe^lR Q[i,g z;NN~pppef[ RicciAmt.RicciAm1uVW Tpef[[HamiltoncQ,N(W1982t^^zNN*N_oNv[t. 2002--2003t^,OV)YMbpef[[Perelman)R(uRicciAm㉳QNPoincares`. vMR(WRicciAmvxvz-N,NNW,gO6ql g㉳Q. ,g z~QRicciAmvW,g'`(TNN͑v6e[e'`[tTBlow-Upb]. v^[vQ-NNNGYpۏLRg. YePgTSfNv B. Chow, P. Lu, L.Ni, Ricci Flow, Ams Graduate Mathematical books. 2006. 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