By Atsushi Kasue (auth.), K. Kenmotsu (eds.)
Read or Download Differential Geometry of Submanifolds: Proceedings of the Conference held at Kyoto, January 23–25, 1984 PDF
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Extra info for Differential Geometry of Submanifolds: Proceedings of the Conference held at Kyoto, January 23–25, 1984
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Helv. R. T. Yau; of manifolds lemma in several 55(1980), Compact with non-positive complex vari- 547-558. group actions curvature, and the topology Topology 18(1979), 361- 380. [26] T. Sunada; Holomorphic mappings symmetric bounded domain, [27] T. Sunada; 51(1979), Rigidity 297-307. into a compact quotient Nagoya Math. J. 64(1976), of certain harmonic mappings, of 159-175. Invent. Math. 36 [28] T. Sunada; Tchebotarev~s in a compact locally density symmetric theorem space for closed of negative geodesics curvature, preprint.
Then, ~ - JT(~). d. existence problem. 2. Theorem. moreover ( [12] ) Suppose T < T*. Then, JT(UT) Proof. 1 and such that ; u ~ BV(~) } . sequence {JT(Uj) } is bounded. {uj} of BV(~). 4) we can d e d u c e that U s i n g the r e s u l t s {u~}j w h i c h c o n v e r g e s F r o m lower topology ( see [3], {uj} is b o u n d e d [ii] where For existence inequality for Iy We give Ax the shall ~ sup l~d ~ II ~ x. ~Id~ll ~Ild~I~. that The in giving case by H u r w i t z curvature an o u t l i n e of It is k n o w n it is e n o u g h easily a geometric as radius get H(M, that if given of in the a bound of #A x. curvature curvature. Riemann A [ 3 ~ ]. of surface N ~ 42 VN/ of T h e o r e m and Ricci the generalization containing ~ for by Y a m a g u c h i a compact #Iso(N) theorem estimate sectional for N) bound negative a partial that -I, with been of a p r o o f embedding to in terms 1N of has 3 is r e g a r d e d Sob olev at VN( 8 ) n of n o n - p o s i t i v i t y of c o m p o n e n t s definite N.