A evolução de Curvas Planas pela Curvatura de Minkowski
A Minkowski plane is a two-dimensional X vector space with a norm || · ||. Three concepts of curvature in this plane are: normal curvature, circular curvature and Minkowski curvature. The main objective of this dissertation is to study the evolution of planar curves by Minkowski curvature. In partic...
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| Format: | master thesis |
| Status: | Published version |
| Publication Date: | 2020 |
| Country: | Brasil |
| Institution: | Universidade Federal de Minas Gerais (UFMG) |
| Repository: | Repositório Institucional da UFMG |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.ufmg.br:1843/39093 |
| Online Access: | http://hdl.handle.net/1843/39093 |
| Access Level: | Open access |
| Keyword: | Plano de Minkowski Tipos de curvatura Curvas com curvatura de Minkowski constante Fluxo pela curvatura de Minkowski Evolução de curvas planas pela curvatura de Minkowski Matemática - Teses Cálculo vetorial - Teses Espaços generalizados - Teses Curvas planas - Teses Superfícies de curvatura constante -Teses |
| Summary: | A Minkowski plane is a two-dimensional X vector space with a norm || · ||. Three concepts of curvature in this plane are: normal curvature, circular curvature and Minkowski curvature. The main objective of this dissertation is to study the evolution of planar curves by Minkowski curvature. In particular, we closed an open gap in the theory of geometric flows of planar curves in Minkowski spaces. For this, we will rst understand geometry of planar curves in Minkowski space following the article ''Concepts of curvatures in normed planes'' [4], which deals with the theory in modern language in a very organized way. Later, using EDP theory, we will show that convex curves evolve over time to constant (non-zero) Minkowski curvature curves. |
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