Minimal Surfaces in Riemannian Manifolds

Β·
Β· American Mathematical Society: Memoirs of the American Mathematical Society αžŸαŸ€αžœαž—αŸ…αž‘αžΈ 495 Β· American Mathematical Soc.
αžŸαŸ€αžœαž—αŸ…β€‹αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž…
50
αž‘αŸ†αž–αŸαžš
αž€αžΆαžšαžœαžΆαž™αžαž˜αŸ’αž›αŸƒ αž“αž·αž„αž˜αžαž·αžœαžΆαž™αžαž˜αŸ’αž›αŸƒαž˜αž·αž“αžαŸ’αžšαžΌαžœαž”αžΆαž“αž•αŸ’αž‘αŸ€αž„αž•αŸ’αž‘αžΆαžαŸ‹αž‘αŸ αžŸαŸ’αžœαŸ‚αž„αž™αž›αŸ‹αž”αž“αŸ’αžαŸ‚αž˜

αž’αŸ†αž–αžΈαžŸαŸ€αžœαž—αŸ…β€‹αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž€αž“αŸαŸ‡

This monograph studies the structure of the set of all co boundary minimal surfaces in Riemannian manifolds. The authors establish, on a solid analytical foundation, a flexible topological index theory which proves useful for the study of minimal surfaces. One of the highlights of the work is the result that for every Jordan curve on the standard $n$-sphere, there exist at least two minimal surfaces bounded by the curve.

αžœαžΆαž™αžαž˜αŸ’αž›αŸƒαžŸαŸ€αžœαž—αŸ…β€‹αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž€αž“αŸαŸ‡

αž”αŸ’αžšαžΆαž”αŸ‹αž™αžΎαž„αž’αŸ†αž–αžΈαž€αžΆαžšαž™αž›αŸ‹αžƒαžΎαž‰αžšαž”αžŸαŸ‹αž’αŸ’αž“αž€αŸ”

αž’αžΆαž“β€‹αž–αŸαžαŸŒαž˜αžΆαž“

αž‘αžΌαžšαžŸαž–αŸ’αž‘αž†αŸ’αž›αžΆαžαžœαŸƒ αž“αž·αž„β€‹αžαŸαž”αŸ’αž›αŸαž
αžŠαŸ†αž‘αžΎαž„αž€αž˜αŸ’αž˜αžœαž·αž’αžΈ Google Play Books αžŸαž˜αŸ’αžšαžΆαž”αŸ‹ Android αž“αž·αž„ iPad/iPhone αŸ” αžœαžΆβ€‹αž’αŸ’αžœαžΎαžŸαž˜αž€αžΆαž›αž€αž˜αŸ’αž˜β€‹αžŠαŸ„αž™αžŸαŸ’αžœαŸαž™αž”αŸ’αžšαžœαžαŸ’αžαž·αž‡αžΆαž˜αž½αž™β€‹αž‚αžŽαž“αžΈβ€‹αžšαž”αžŸαŸ‹αž’αŸ’αž“αž€β€‹ αž“αž·αž„β€‹αž’αž“αž»αž‰αŸ’αž‰αžΆαžαž±αŸ’αž™β€‹αž’αŸ’αž“αž€αž’αžΆαž“αž–αŸαž›β€‹αž˜αžΆαž“αž’αŸŠαžΈαž“αž’αžΊαžŽαž·αž αž¬αž‚αŸ’αž˜αžΆαž“β€‹αž’αŸŠαžΈαž“αž’αžΊαžŽαž·αžβ€‹αž“αŸ…αž‚αŸ’αžšαž”αŸ‹αž‘αžΈαž€αž“αŸ’αž›αŸ‚αž„αŸ”
αž€αž»αŸ†αž–αŸ’αž™αžΌαž‘αŸαžšβ€‹αž™αž½αžšαžŠαŸƒ αž“αž·αž„αž€αž»αŸ†αž–αŸ’αž™αžΌαž‘αŸαžš
αž’αŸ’αž“αž€αž’αžΆαž…αžŸαŸ’αžŠαžΆαž”αŸ‹αžŸαŸ€αžœαž—αŸ…αž‡αžΆαžŸαŸ†αž‘αŸαž„αžŠαŸ‚αž›αž”αžΆαž“αž‘αž·αž‰αž“αŸ…αž€αŸ’αž“αž»αž„ Google Play αžŠαŸ„αž™αž”αŸ’αžšαžΎαž€αž˜αŸ’αž˜αžœαž·αž’αžΈαžšαž»αž€αžšαž€αžαžΆαž˜αž’αŸŠαžΈαž“αž’αžΊαžŽαž·αžαž€αŸ’αž“αž»αž„αž€αž»αŸ†αž–αŸ’αž™αžΌαž‘αŸαžšαžšαž”αžŸαŸ‹αž’αŸ’αž“αž€αŸ”
eReaders αž“αž·αž„β€‹αž§αž”αž€αžšαžŽαŸβ€‹αž•αŸ’αžŸαŸαž„β€‹αž‘αŸ€αž
αžŠαžΎαž˜αŸ’αž”αžΈαž’αžΆαž“αž“αŸ…αž›αžΎβ€‹αž§αž”αž€αžšαžŽαŸ e-ink αžŠαžΌαž…αž‡αžΆβ€‹αž§αž”αž€αžšαžŽαŸαž’αžΆαž“β€‹αžŸαŸ€αžœαž—αŸ…αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž€ Kobo αž’αŸ’αž“αž€αž“αžΉαž„αžαŸ’αžšαžΌαžœβ€‹αž‘αžΆαž‰αž™αž€β€‹αž―αž€αžŸαžΆαžš αž αžΎαž™β€‹αž•αŸ’αž‘αŸαžšαžœαžΆαž‘αŸ…β€‹αž§αž”αž€αžšαžŽαŸβ€‹αžšαž”αžŸαŸ‹αž’αŸ’αž“αž€αŸ” αžŸαžΌαž˜αž’αž“αž»αžœαžαŸ’αžαžαžΆαž˜β€‹αž€αžΆαžšαžŽαŸ‚αž“αžΆαŸ†αž›αž˜αŸ’αž’αž·αžαžšαž”αžŸαŸ‹αž˜αž‡αŸ’αžˆαž˜αžŽαŸ’αžŒαž›αž‡αŸ†αž“αž½αž™ αžŠαžΎαž˜αŸ’αž”αžΈαž•αŸ’αž‘αŸαžšαž―αž€αžŸαžΆαžšβ€‹αž‘αŸ…αž§αž”αž€αžšαžŽαŸαž’αžΆαž“αžŸαŸ€αžœαž—αŸ…β€‹αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž€αžŠαŸ‚αž›αžŸαŸ’αž‚αžΆαž›αŸ‹αŸ”