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Identifier 000398254
Title Monotone quantities on complete riemannian manifolds with non-negative Ricci curvature
Alternative Title Μονότονες ποσότητες σε πλήρεις πολλαπλότητες Riemman με μη αρνητική καμπυλότητα Ricci
Author Τοπουκτζίδης, Θεόφιλος
Thesis advisor Φίλιππας, Στάθης
Reviewer Τέρτικας, Αχιλλέας
Πλατής, Ιωάννης
Abstract In the current thesis we consider an n-dimensional non-compact and complete Rie-mannian manifold with n > 3. We then present three new monotonicity formulas which involve quantities that can be thought of as generalized normalized area and volume of balls in our manifold. Using these new monotonicity formulas, we derive a new gradient estimate for the Green function which improves a previous estimate by Cheng and Yau. The present work is based on the study of a recent paper by Tobias H. Colding [5], as well as the use of standard results of geometric analysis such as the Bishop-Gromov theorem and the Bochner-Weitzenbock formula.
Language English
Subject Gradient estimates
Green function
Monotonicity formulas
Μονότονες φόρμουλες
Συνάρτηση Green
Issue date 2015-11-20
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
  Type of Work--Post-graduate theses
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