Thesis /

ROMDOC-THESIS-2016-520

Hessian structures, special functions and evolution metrics

Corcodel, Claudiu
2010-04-16

Abstract: Rezumat al tezei de doctorat “Hessian structures, special functions and evolution metrics” drd. Claudiu Corcodel Studiul structurilor Hessiene si al aplicatiilor acestora in stiintele experimentale este o preocupare de actualitate a unor cercetatori cunoscuti din Japonia, Anglia, Romania, Australia, Belgia, Canada etc. Avem in vedere lucrari de data recenta semnate de H. Shima, B. Totaro, C. Udriste, D. Jiang, P. L. Antonelli, S. Amari, Y. Nesterov si altii. Baza structurilor Hessiene o reprezinta metricile Riemanniene Hessiene, adica metrici Riemanniene exprimate ca Hessiana unei functii raportata la o alta metrica Riemanniana. Lucrarea pune laolalta rezultate originale privind structurile Hessiene si face legaturi originale cu functiile speciale si metricile de evolutie. Este structurata in sase capitole, plus un rezumat in limbile romana si engleza. Fiecare capitol este elaborat avand la baza o lucrare publicata. Fructificand cadrul fertil oferit de notiunea de structura Hessiana, lucrarea aduce importante contributii teoretice la dezvoltarea acestora si face semnifcative conexiuni cu modelarea matematica, teoria optimizarilor, fizica matematica, statistica. Studiul include: structuri de tip Hessian pe varietati pseudo-Riemanniene, functii autoconcordante pe varietati Riemanniene, structuri Hessiene bidimensionale pe varietati Riemanniene, caracteristici geometrice ale functiilor speciale, metrici de evolutie si campuri vectoriale geometrice, o abordare geometrica a principiului de maxim. Abstract of Ph. D. Thesis “Hessian structures, special functions and evolution metrics” by Claudiu Corcodel The study of Hessian structures and of their applications in experimental sciences is a topical interest of known scientists from Japan, England, Romania, Australia, Belgium, Canada etc. We have in view some recent works by H. Shima, B. Totaro, C. Udriste, P. L. Antonelli, S. Amari, D. Jiang, Y. Nesterov and others. The basis of Hessian structures is represented by Hessian Riemannian metrics, that is Riemannian metrics expressed as the Hessian of a function with respect to another Riemannian metric. This work holds together original results concerning Hessian structures and makes original connections with special functions and evolution metrics. It has six chapters and two abstracts, one in Romanian, the other in English. Each chapter has as basis a published paper. Taking advantage of the fertile framework given by the notion of Hessian, the work brings important contributions to its development and makes significant connections with Mathematical Modeling, Optimization Theory, Mathematical Physics and Statistics. The study includes: Hessian type structures on pseudo-Riemannian manifolds, self-concordant functions on Riemannian manifolds, 2D Hessian structures on Riemannian manifolds, geometric characteristics of special functions, evolution metrics and geometric vector fields, a geometric approach of maximum principle.

Keyword(s): Structuri Hessiene (Matematică) -- Teză de doctorat ; Spaţii Riemann -- Geometrie diferenţială -- Teză de doctorat
OPAC: See record in BC-UPB Web OPAC
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