2026-09-23T16:37:38Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/50692 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Tumanov, Alexander Kerman, Ely Tumanov, Alexander D’Angelo, John Tolman, Susan Wong, Yat Sen 2014-09-16T17:25:20Z 2014-09-16T17:25:20Z 2014-08 2014-09-16 2014-08 This thesis covers four results: 1. We prove an analog of Whitney's embedding theorem for J-holomorphic discs. 2. For zj = xj + i*yj in C and let D_R^2 = {(z1, z2) in C^2 : x1^2 + x2^2 <1, y1^2 + y2^2 < 1} be the real bi-disc in C^2. We find the sharp lower bound for R such that D_R^2 admits a symplectic embedding into D(R) * C, the complex cylinder with base radius R. The sharp lower bound for R is shown to be 2/sqrt(pi). As a consequence, we know that D_R^2 and D^2 are not symplectomorphic. 3. We extend the second result by showing that if T is an orthogonal matrix on R^4 = C^2, then TD^2 is symplectomorphic to D^2 if and only if T is unitary or conjugate to unitary. 4. A high dimensional case of the second result: for r >= 1 and n >= 2, we show that D_R^2 * D^(n-2)(r) and D^2 * D^(n-2)(r) are not symplectomorphic. Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-06-11T13:32:45Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 WONG_YATSEN.pdf: 330480 bytes, checksum: f4bc51e7fa980d8637ad39d7ef27591c (MD5) WONG_YATSEN.zip: 27493 bytes, checksum: 4cc485cd461b58c919b555c722a3b8f6 (MD5) WONG_YATSEN.pdf: 330489 bytes, checksum: e963616d737b8955190e7464483927fa (MD5) Made available in DSpace on 2014-09-16T17:25:20Z (GMT). No. of bitstreams: 3 Yat Sen_Wong.pdf: 330465 bytes, checksum: 3a881f2580e4b45ce958b44fb5a4ccef (MD5) WONG_YATSEN.zip: 27491 bytes, checksum: 5baa65d8bfaa0af310e1487f73ec7b32 (MD5) license.txt: 4060 bytes, checksum: e979ec359afc71a6caa8d6448e37a375 (MD5) http://hdl.handle.net/2142/50692 en Copyright 2014 Yat Sen Wong J-holomorphic curve symplectic embedding symplectomorphism J - holomorphic curves and their applications text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD