In this thesis we present a slight generalisation of the Pearl complex or relative quantum homology to some non monotone Lagrangian submanifolds. First we develop the theory for the so called almost monotone Lagrangian submanifolds, We apply it to uniruling problems as well as estimates for the relative Gromov width. In the second part we develop the theory for toric fiber in toric Fano manifolds, recovering previous computaional results of Floer homology . / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

<p>The research topic of this PhD thesis is a comparative analysis of classical specic&nbsp;geometric frameworks and of their anisotropic extensions; the construction of three different&nbsp;types of Finsler frameworks, which are suitable for the analysis of the cancer cells population&nbsp;dynamical system; the development of the anisotropic Beltrami framework theory with the&nbsp;derivation of the evolution&nbsp;ow equations corresponding to different classes of anisotropic&nbsp;metrics, and tentative applications in image processing.</p> / <p>Predmet istraživanja doktorske disertacije je uporedna analiza klasičnih i specifičnih&nbsp;geometrijskih radnih okruženja i njihovih anizotropnih pro&scaron;irenja; konstrukcija &nbsp;tri Finslerova&nbsp;radna okruženja različitog tipa koja su pogodna za analizu dinamičkog &nbsp;sistema populacije&nbsp;kanceroznih ćelija; razvoj teorije anizotropnog Beltramijevog radnog okruženja i formiranje&nbsp;jednačina evolutivnog toka za različite klase anizotropnih metrika, kao i mogućnost primene&nbsp;dobijenih teorijskih rezultata u digitalnoj obradi slika.</p>