id	sid	tid	token	lemma	pos
0z708w35p5f	1	1	we	we	PRON
0z708w35p5f	1	2	define	define	VERB
0z708w35p5f	1	3	and	and	CCONJ
0z708w35p5f	1	4	explore	explore	VERB
0z708w35p5f	1	5	various	various	ADJ
0z708w35p5f	1	6	properties	property	NOUN
0z708w35p5f	1	7	of	of	ADP
0z708w35p5f	1	8	a	a	DET
0z708w35p5f	1	9	generalization	generalization	NOUN
0z708w35p5f	1	10	of	of	ADP
0z708w35p5f	1	11	poincaré	poincaré	PROPN
0z708w35p5f	1	12	-	-	PUNCT
0z708w35p5f	1	13	type	type	NOUN
0z708w35p5f	1	14	kähler	kähler	PROPN
0z708w35p5f	1	15	metrics	metric	NOUN
0z708w35p5f	1	16	defined	define	VERB
0z708w35p5f	1	17	on	on	ADP
0z708w35p5f	1	18	the	the	DET
0z708w35p5f	1	19	complement	complement	NOUN
0z708w35p5f	1	20	of	of	ADP
0z708w35p5f	1	21	a	a	DET
0z708w35p5f	1	22	complex	complex	ADJ
0z708w35p5f	1	23	hypersurface	hypersurface	NOUN
0z708w35p5f	1	24	x	x	PUNCT
0z708w35p5f	1	25	embedded	embed	VERB
0z708w35p5f	1	26	in	in	ADP
0z708w35p5f	1	27	an	an	DET
0z708w35p5f	1	28	ambient	ambient	ADJ
0z708w35p5f	1	29	kähler	kähler	NOUN
0z708w35p5f	1	30	manifold	manifold	PROPN
0z708w35p5f	1	31	n.	n.	PROPN
0z708w35p5f	1	32	after	after	ADP
0z708w35p5f	1	33	motivating	motivate	VERB
0z708w35p5f	1	34	interest	interest	NOUN
0z708w35p5f	1	35	in	in	ADP
0z708w35p5f	1	36	a	a	DET
0z708w35p5f	1	37	generalization	generalization	NOUN
0z708w35p5f	1	38	,	,	PUNCT
0z708w35p5f	1	39	especially	especially	ADV
0z708w35p5f	1	40	from	from	ADP
0z708w35p5f	1	41	the	the	DET
0z708w35p5f	1	42	viewpoint	viewpoint	NOUN
0z708w35p5f	1	43	of	of	ADP
0z708w35p5f	1	44	extremal	extremal	ADJ
0z708w35p5f	1	45	kähler	kähler	PROPN
0z708w35p5f	1	46	geometry	geometry	NOUN
0z708w35p5f	1	47	,	,	PUNCT
0z708w35p5f	1	48	we	we	PRON
0z708w35p5f	1	49	construct	construct	VERB
0z708w35p5f	1	50	a	a	DET
0z708w35p5f	1	51	distortion	distortion	NOUN
0z708w35p5f	1	52	potential	potential	NOUN
0z708w35p5f	1	53	ψτ	ψτ	PROPN
0z708w35p5f	1	54	v	v	NOUN
0z708w35p5f	1	55	christened	christen	VERB
0z708w35p5f	1	56	the	the	DET
0z708w35p5f	1	57	gnarl	gnarl	NOUN
0z708w35p5f	1	58	associated	associate	VERB
0z708w35p5f	1	59	to	to	ADP
0z708w35p5f	1	60	the	the	DET
0z708w35p5f	1	61	vector	vector	NOUN
0z708w35p5f	1	62	field	field	NOUN
0z708w35p5f	1	63	v	v	NOUN
0z708w35p5f	1	64	due	due	ADP
0z708w35p5f	1	65	to	to	ADP
0z708w35p5f	1	66	its	its	PRON
0z708w35p5f	1	67	simulation	simulation	NOUN
0z708w35p5f	1	68	of	of	ADP
0z708w35p5f	1	69	flowing	flow	VERB
0z708w35p5f	1	70	along	along	ADP
0z708w35p5f	1	71	level	level	NOUN
0z708w35p5f	1	72	sets	set	NOUN
0z708w35p5f	1	73	of	of	ADP
0z708w35p5f	1	74	τ	τ	PROPN
0z708w35p5f	1	75	in	in	ADP
0z708w35p5f	1	76	the	the	DET
0z708w35p5f	1	77	direction	direction	NOUN
0z708w35p5f	1	78	of	of	ADP
0z708w35p5f	1	79	v	v	NOUN
0z708w35p5f	1	80	upon	upon	SCONJ
0z708w35p5f	1	81	approaching	approaching	PROPN
0z708w35p5f	1	82	x.	x.	PROPN
0z708w35p5f	1	83	key	key	ADJ
0z708w35p5f	1	84	subexponential	subexponential	ADJ
0z708w35p5f	1	85	estimates	estimate	NOUN
0z708w35p5f	1	86	are	be	AUX
0z708w35p5f	1	87	derived	derive	VERB
0z708w35p5f	1	88	to	to	PART
0z708w35p5f	1	89	relate	relate	VERB
0z708w35p5f	1	90	the	the	DET
0z708w35p5f	1	91	gnarled	gnarled	ADJ
0z708w35p5f	1	92	metric	metric	NOUN
0z708w35p5f	1	93	to	to	ADP
0z708w35p5f	1	94	a	a	DET
0z708w35p5f	1	95	starting	start	VERB
0z708w35p5f	1	96	poincaré	poincaré	ADJ
0z708w35p5f	1	97	-	-	PUNCT
0z708w35p5f	1	98	type	type	NOUN
0z708w35p5f	1	99	metric	metric	NOUN
0z708w35p5f	1	100	,	,	PUNCT
0z708w35p5f	1	101	allowing	allow	VERB
0z708w35p5f	1	102	us	we	PRON
0z708w35p5f	1	103	to	to	PART
0z708w35p5f	1	104	prove	prove	VERB
0z708w35p5f	1	105	statements	statement	NOUN
0z708w35p5f	1	106	about	about	ADP
0z708w35p5f	1	107	the	the	DET
0z708w35p5f	1	108	volume	volume	NOUN
0z708w35p5f	1	109	and	and	CCONJ
0z708w35p5f	1	110	integrals	integral	NOUN
0z708w35p5f	1	111	of	of	ADP
0z708w35p5f	1	112	the	the	DET
0z708w35p5f	1	113	curvatures	curvature	NOUN
0z708w35p5f	1	114	of	of	ADP
0z708w35p5f	1	115	the	the	DET
0z708w35p5f	1	116	gnarled	gnarled	NOUN
0z708w35p5f	1	117	metric.to	metric.to	NUM
0z708w35p5f	1	118	relate	relate	VERB
0z708w35p5f	1	119	the	the	DET
0z708w35p5f	1	120	gnarling	gnarl	VERB
0z708w35p5f	1	121	construction	construction	NOUN
0z708w35p5f	1	122	to	to	ADP
0z708w35p5f	1	123	the	the	DET
0z708w35p5f	1	124	extremal	extremal	ADJ
0z708w35p5f	1	125	setting	setting	NOUN
0z708w35p5f	1	126	,	,	PUNCT
0z708w35p5f	1	127	we	we	PRON
0z708w35p5f	1	128	prove	prove	VERB
0z708w35p5f	1	129	a	a	DET
0z708w35p5f	1	130	local	local	ADJ
0z708w35p5f	1	131	perturbation	perturbation	NOUN
0z708w35p5f	1	132	result	result	NOUN
0z708w35p5f	1	133	showing	show	VERB
0z708w35p5f	1	134	the	the	DET
0z708w35p5f	1	135	existence	existence	NOUN
0z708w35p5f	1	136	of	of	ADP
0z708w35p5f	1	137	csck	csck	ADJ
0z708w35p5f	1	138	gnarled	gnarl	VERB
0z708w35p5f	1	139	metrics	metric	NOUN
0z708w35p5f	1	140	in	in	ADP
0z708w35p5f	1	141	kähler	kähler	PROPN
0z708w35p5f	1	142	classes	class	NOUN
0z708w35p5f	1	143	near	near	ADP
0z708w35p5f	1	144	to	to	ADP
0z708w35p5f	1	145	that	that	PRON
0z708w35p5f	1	146	of	of	ADP
0z708w35p5f	1	147	a	a	DET
0z708w35p5f	1	148	standard	standard	ADJ
0z708w35p5f	1	149	product	product	NOUN
0z708w35p5f	1	150	metric	metric	NOUN
0z708w35p5f	1	151	on	on	ADP
0z708w35p5f	1	152	n	n	PROPN
0z708w35p5f	1	153	\	\	X
0z708w35p5f	1	154	x	x	PROPN
0z708w35p5f	1	155	,	,	PUNCT
0z708w35p5f	1	156	providing	provide	VERB
0z708w35p5f	1	157	a	a	DET
0z708w35p5f	1	158	significant	significant	ADJ
0z708w35p5f	1	159	step	step	NOUN
0z708w35p5f	1	160	towards	towards	ADP
0z708w35p5f	1	161	developing	develop	VERB
0z708w35p5f	1	162	more	more	ADJ
0z708w35p5f	1	163	general	general	ADJ
0z708w35p5f	1	164	openness	openness	NOUN
0z708w35p5f	1	165	properties	property	NOUN
0z708w35p5f	1	166	for	for	ADP
0z708w35p5f	1	167	extremal	extremal	ADJ
0z708w35p5f	1	168	gnarled	gnarl	VERB
0z708w35p5f	1	169	metrics	metric	NOUN
0z708w35p5f	1	170	.	.	PUNCT
0z708w35p5f	2	1	we	we	PRON
0z708w35p5f	2	2	discuss	discuss	VERB
0z708w35p5f	2	3	the	the	DET
0z708w35p5f	2	4	challenges	challenge	NOUN
0z708w35p5f	2	5	of	of	ADP
0z708w35p5f	2	6	adapting	adapt	VERB
0z708w35p5f	2	7	the	the	DET
0z708w35p5f	2	8	gnarl	gnarl	NOUN
0z708w35p5f	2	9	to	to	ADP
0z708w35p5f	2	10	the	the	DET
0z708w35p5f	2	11	global	global	ADJ
0z708w35p5f	2	12	situation	situation	NOUN
0z708w35p5f	2	13	of	of	ADP
0z708w35p5f	2	14	embedding	embed	VERB
0z708w35p5f	2	15	x	x	PROPN
0z708w35p5f	2	16	in	in	ADP
0z708w35p5f	2	17	a	a	DET
0z708w35p5f	2	18	compact	compact	ADJ
0z708w35p5f	2	19	kähler	kähler	NOUN
0z708w35p5f	2	20	manifold	manifold	PROPN
0z708w35p5f	2	21	m	m	PROPN
0z708w35p5f	2	22	,	,	PUNCT
0z708w35p5f	2	23	consider	consider	VERB
0z708w35p5f	2	24	the	the	DET
0z708w35p5f	2	25	case	case	NOUN
0z708w35p5f	2	26	that	that	SCONJ
0z708w35p5f	2	27	n	n	CCONJ
0z708w35p5f	2	28	is	be	AUX
0z708w35p5f	2	29	the	the	DET
0z708w35p5f	2	30	disk	disk	NOUN
0z708w35p5f	2	31	bundle	bundle	NOUN
0z708w35p5f	2	32	of	of	ADP
0z708w35p5f	2	33	an	an	DET
0z708w35p5f	2	34	hermitian	hermitian	ADJ
0z708w35p5f	2	35	line	line	NOUN
0z708w35p5f	2	36	bundle	bundle	NOUN
0z708w35p5f	2	37	over	over	ADP
0z708w35p5f	2	38	x	x	PROPN
0z708w35p5f	2	39	,	,	PUNCT
0z708w35p5f	2	40	and	and	CCONJ
0z708w35p5f	2	41	lastly	lastly	ADV
0z708w35p5f	2	42	proposing	propose	VERB
0z708w35p5f	2	43	some	some	DET
0z708w35p5f	2	44	open	open	ADJ
0z708w35p5f	2	45	problems	problem	NOUN
0z708w35p5f	2	46	and	and	CCONJ
0z708w35p5f	2	47	avenues	avenue	NOUN
0z708w35p5f	2	48	for	for	ADP
0z708w35p5f	2	49	further	further	ADJ
0z708w35p5f	2	50	work	work	NOUN
0z708w35p5f	2	51	using	use	VERB
0z708w35p5f	2	52	gnarls	gnarl	NOUN
0z708w35p5f	2	53	.	.	PUNCT