228 KB606 KB122 KB1994Černe, MiranForstnerič, Franc124 straniCOBISSID:238083840URN:URN:NBN:SI:doc-OEY7ZI1AendLib distributerM. Černevisokošolska delaanalitični selektorjiCR-mnogoterostdefektfibracijakompleksna analizakonormalni svežnjiLagrangejeva podmnogoterostminimalni diskiparcialni indeksipolinomska ogrinjačaregular discsuregularni diskistacionarni diskiAnalytic discs with boundaries in a generating CR-manifold| a thesis submitted in partial fulfillment of the requirements for the degree of doctor of philosophy (mathematics)|The problem of perturbing analytic discs with boundary in CR-submanifold of ?$\Cc^n$? is considered. A theorem by globevnik on the perturbation by analytic discs along maximal real submanifolds of ?$\Cc^n$? is generalized and used in various applications: (i) it is proved that every energy functional minimizing disc in ?$\Cc^n$? with free boundary in a Lagrangian submanifold of ?$\Cc^n$? and all partial indices greater or equal -1 is holomorphic, (ii) a new proof and a generalization of a result by Pang on the Kobayashi extremal discs is given, (iii) perturbations of analytic varieties with boundaries in a totally real torus in ?$\Cc^2$? fibered over the unit circle ?$\partial D$? are considered. Also, some results by Baouendi, Rothschild and Trepreau on the family of analytic discs attached to a CR-submanifold of ?$\Cc^n$? of a positive CR-dimension are globalizedObravnavamo problem perturbacije analitičnih diskov z robovi v CR-mnogoterosti. Globevnikov izrek o perturbaciji analitičnega diska vzdolž maksimalno realne mnogoterosti v ?$\Cc^n$? posplošimo in uporabimo v raznih aplikacijah. (i) Dokažemo, da je vsak disk, ki minimizira energijski funkcional in ima svoj rob vsebovan v dani Lagrangejevi podmnogoterosti ?$\Cc^n$?, pri pogoju, da so njegovi parcialni indeksi večji ali enaki -1, holomorfen. (ii) Podan je nov dokaz in posplošitev rezultatov Panga in Kobayashija o ekstremalnih diskih. (iii) Obravnavamo perturbacije analitičnih množic z robovi v totalno realnih torusih. Globaliziramo tudi nekatere Baouendijeve, Rothschildove in Tepreaujeve rezultate o družini analitičnih diskov, ki so pritrjeni k CR-podmnogoterosti ?$\Cc^n$? s pozitivno CR-dimenzijodoktorska disertacijaTEXTvisokošolska delatheses and dissertationsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza v Ljubljani, Fakulteta za matematiko in fiziko