Conformal invariants and partial differential equations
نویسندگان
چکیده
منابع مشابه
Conformal Invariants and Partial Differential Equations
Our goal is to study quantities in Riemannian geometry which remain invariant under the “conformal change of metrics”–that is, under changes of metrics which stretch the length of vectors but preserve the angles between any pair of vectors. We call such a quantity “conformally invariant”. In conjunction with the study of conformal invariants, we are also interested in studying “conformally cova...
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در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Invariants and Symmetries for Partial Differential Equations and Lattices
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as Mathematica. Invariants and symmetries are shown for several well-known equations. Our Mathematica package allows one to automatically compute invariants and symmetri...
متن کاملNon-linear Partial Differential Equations in Conformal Geometry
In the study of conformal geometry, the method of elliptic partial differential equations is playing an increasingly significant role. Since the solution of the Yamabe problem, a family of conformally covariant operators (for definition, see section 2) generalizing the conformal Laplacian, and their associated conformal invariants have been introduced. The conformally covariant powers of the La...
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We show that, for both the conformal and projective groups, all the differential invariants of a generic surface in three-dimensional space can be written as combinations of the invariant derivatives of a single differential invariant. The proof is based on the equivariant method of moving frames.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2005
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-05-01058-x