| Preface | p. V |
| Sign-Changing Yamabe-Type Problems | p. 1 |
| General Introduction | p. 1 |
| Results and Conditions | p. 2 |
| Conjecture 2 and Sketch of the Proof of Theorem 1; Outline | p. 7 |
| The Difference of Topology | p. 11 |
| Open Problems | p. 14 |
| Understand the difference of topology | p. 14 |
| Non critical asymptots | p. 15 |
| The exit set from infinity | p. 15 |
| Establishing Conjecture 2 and continuous forms of the discrete inequality | p. 16 |
| The Morse Lemma at infinity, Part I, II, III | p. 16 |
| Notations v, v[subscript i], h[subscript i] | p. 16 |
| Preliminary Estimates and Expansions, the Principal Terms | p. 17 |
| Preliminary Estimates | p. 18 |
| The equation satisfied by v | p. 19 |
| First estimates on v[subscript i] and h[subscript i] | p. 23 |
| The matrix A | p. 25 |
| Towards an H[Characters not reproducible]-estimate on v[subscript i]i and an L[superscript infinity]-estimate on h[subscript i] | p. 26 |
| The formal estimate on h[subscript i] | p. 31 |
| Remarks about the basic estimates | p. 35 |
| Estimating the right hand side of Lemma 12 | p. 35 |
| R[subscript i] and the estimate on v[subscript i] [subscript H Characters not reproducible] | p. 45 |
| Proof of the Morse Lemma at Infinity When the Concentrations are Comparable | p. 54 |
| Redirecting the Estimates, Estimates on v[subscript i] [subscript H Characters not reproducible] + h[Characters not reproducible] [subscript infinity] + [Characters not reproducible] [epsilon Characters not reproducible] h[Characters not reproducible] [subscript infinity] | p. 66 |
| Content of Part II | p. 66 |
| Redirecting the estimates | p. 68 |
| Proof of the Morse Lemma at Infinity | p. 108 |
| Decomposition in groups, gradient and L[superscript infinity]-estimates on v, proof of the Morse Lemma at infinity | p. 108 |
| Content of Part III | p. 108 |
| Basic conformally invariant estimates | p. 109 |
| Estimates on v - (v[subscript I] + v[subscript II]) | p. 121 |
| The expansion | p. 129 |
| The coefficient in front of [epsilon subscript k Characters not reproducible][delta subscript Characters not reproducible] | p. 154 |
| The [sigma subscript i] equation, the estimate on [Sigma] [gamma Characters not reproducible] | p. 159 |
| The system of equations corresponding to the variations of the points a[subscript i] | p. 174 |
| Rule about the variation of the points of concentrations of the various groups | p. 182 |
| The basic parameters and the end of the expansion | p. 185 |
| Remarks on the basic parameters | p. 185 |
| The end of the expansion and the concluding remarks | p. 189 |
| Bibliography | p. 199 |
| Contact Form Geometry | p. 201 |
| General Introduction | p. 201 |
| On the Dynamics of a Contact Structure along a Vector Field of its Kernel | p. 205 |
| Introduction | p. 205 |
| Introducing a large rotation | p. 210 |
| How [gamma] is built | p. 214 |
| Modification of [alpha] into [alpha subscript N] | p. 226 |
| Computation of [xi subscript N] | p. 227 |
| Conformal deformation | p. 235 |
| Choice of [lambda] | p. 240 |
| First step in the construction of [lambda] | p. 241 |
| Appendix 1 | p. 275 |
| The normal form for ([alpha], v) when [alpha] does not turn well | p. 275 |
| The Normal Form of ([alpha], v) Near an Attractive Periodic Orbit of v | p. 276 |
| Compactness | p. 279 |
| Some basic facts | p. 280 |
| A model for W[subscript u](x[subscript m]), the unstable manifold in C[subscript beta] of a periodic orbit of index m | p. 282 |
| Hypothesis (A), Hypothesis (B), Statement of the result | p. 288 |
| The hole flow | p. 291 |
| Combinatorics | p. 291 |
| Normals | p. 294 |
| Hole flow and Normal (II)-flow on curves of [Gamma subscript 4k] near x[superscript infinity] | p. 296 |
| Forced repetition | p. 299 |
| The Global picture, the degree is zero | p. 301 |
| Companions | p. 304 |
| Their definition, births and deaths | p. 304 |
| Families and nodes | p. 305 |
| Flow-lines for x[subscript 2k+1] to x[Characters not reproducible] | p. 323 |
| The S[superscript 1]-classifying map | p. 332 |
| Small and high oscillation, consecutive characteristic pieces | p. 334 |
| Iterates of critical points at infinity | p. 354 |
| The Fredholm aspect | p. 359 |
| Transversality and the compactness argument | p. 364 |
| Transmutations | p. 384 |
| Study of the Poincare-return maps | p. 402 |
| Definition of a basis of T[subscript x subscript infinity] [Gamma subscript 2s] for the reduction of d[superscript 2] J(x[subscript infinity]) | p. 413 |
| Compatibility | p. 417 |
| On the Morse Index of a Functional Arising in Contact Form Geometry | p. 420 |
| Introduction | p. 420 |
| The Case of [Gamma subscript 2] | p. 424 |
| Darboux Coordinates | p. 425 |
| The v-transport maps | p. 430 |
| The equations of the characteristic manifold near x[superscript infinity]; the equations of a critical point | p. 434 |
| The characteristic manifold for the unperturbed problem | p. 434 |
| Critical points, vanishing of the determinant | p. 436 |
| Introducing the perturbation | p. 437 |
| The characteristic manifold for the perturbed problem; the determinant equations | p. 441 |
| Reduction to the Case k = 1 | p. 447 |
| Modification of d[superscript 2]J[Characters not reproducible](x[subscript infinity]) [subscript span{u[subscript 2]...,u[subscript k-1]}] | p. 454 |
| Calculation of [Characters not reproducible superscript 2]J[subscript infinity](x[subscript infinity]).u[subscript 2].u[subscript 3] | p. 459 |
| Calculation of [Characters not reproducible superscript 2]J[subscript infinity](x[subscript infinity]).u[subscript 2].u[subscript 2] | p. 465 |
| Calculation of [Characters not reproducible superscript 2]J[subscript infinity](x[subscript infinity]).u[subscript 2].u[subscript 4] | p. 471 |
| Other Second Order Derivatives | p. 474 |
| Appendix | p. 476 |
| The Proof of Lemma 42 | p. 476 |
| The proof of Lemma 47 | p. 480 |
| Proof of the Lemmas in 2.7.11 | p. 483 |
| Proof of Lemma 48 | p. 483 |
| The Proof of Lemma 49 | p. 484 |
| The proof of Lemma 50 | p. 485 |
| Proof of Claim 1 | p. 487 |
| Proof of Claim 3 | p. 489 |
| The Final Details of the Calculation of [Characters not reproducible superscript 2]J(x[subscript infinity]).u[subscript 2].u[subscript 3] | p. 492 |
| Details involved in 2.8 | p. 494 |
| Proof of Lemma 52 | p. 494 |
| Proof of Lemma 53 | p. 495 |
| Proof of Claim 3 | p. 496 |
| Proof of Claim 4 | p. 497 |
| Details of the Calculation of [Characters not reproducible superscript 2]J.u[subscript 2].u[subscript 2] | p. 503 |
| Bibliography | p. 509 |
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