By Vladimir Rovenski, Pawel Walczak

This quantity has been divided into components: Geometry and purposes. The geometry component of the e-book relates essentially to geometric flows, laminations, necessary formulae, geometry of vector fields on Lie teams and osculation; the articles within the purposes component drawback a few specific difficulties of the idea of dynamical structures, together with mathematical difficulties of liquid flows and a learn of cycles for non-dynamical systems.

This paintings relies at the moment overseas workshop entitled "Geometry and Symbolic Computations," hung on may well 15-18, 2013 on the college of Haifa and is devoted to modeling (using symbolic calculations) in differential geometry and its functions in fields equivalent to desktop technological know-how, tomography and mechanics. it's meant to create a discussion board for college kids and researchers in natural and utilized geometry to advertise dialogue of recent cutting-edge in geometric modeling utilizing symbolic courses similar to Maple™ and Mathematica® , in addition to presentation of latest results.

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4. a1 ; a2 ; a3 / D 0g (see Sects. 5 and 7). The following questions are worth for further investigation. Question 1. x1 ; x2 / of system (5). 0; 1=23 . We specify the above question for some other partial cases. Question 2. 0; 1=2, i ¤ j ¤ k ¤ i . Question 3. 0; 1=2/3? Question 4. a1 ; a2 ; a3 / of the surface at least two degenerate singular points of (5)? 0; 1=2/3 with Acknowledgements The authors are indebted to Prof. Yusuke Sakane for useful discussions concerning computational aspects of this project and to Tanya Nikonorova for her help with the graphics.

0; 1=2/3? Question 4. a1 ; a2 ; a3 / of the surface at least two degenerate singular points of (5)? 0; 1=2/3 with Acknowledgements The authors are indebted to Prof. Yusuke Sakane for useful discussions concerning computational aspects of this project and to Tanya Nikonorova for her help with the graphics. 1) and by Federal Target Grant “Scientific and educational personnel of innovative Russia” for 2009–2013 (agreement no. 8206, application no. 1-12-000-1003-014). A. Abiev et al. References 1. , Siasos P.

X/ D 1 2 2 n 2 x on RnCp . / n 2 FO > C e n 2t H: By (15), the second fundamental tensors of FO and F are related by hO D e 2 hence, HO D e n t H . d tO=dt/ @FO @FO D O @t @t dt D n d tO 2 2n e 2t 2n 1 2t HO : D e 2n 1 tO FO > C HO D 2 n 2t h; (16) 2t 1 2n , and Á 2 1 FO > C HO : (17) Gaussian Mean Curvature Flow for Submanifolds in Space Forms 45 Flow (17) is, up to a tangential diffeomorphism (see Remark 1), equivalent to the MCF equation @t FO D HO for tO < TO D 12 n 2 (because at TO the tangential diffeomorphism giving the equivalence is not well defined: the time tO D TO corresponds in (13) to t D 1).

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