# Mathematical Sciences Research Institute

Home » Geometry and Analysis of Surface Group Representations: The Area of Convex Projective 2-Orbifolds

# Seminar

Geometry and Analysis of Surface Group Representations: The Area of Convex Projective 2-Orbifolds April 22, 2015 (11:00 AM PDT - 12:30 PM PDT)
Parent Program: Dynamics on Moduli Spaces of Geometric Structures MSRI: Baker Board Room
The Hilbert metric on a bounded convex set $\Omega\subset\mathbb R^2$ determines an area 2-form on $\Omega$. One of the coordinates used by Fock and Goncharov assigns to an ideal triangle $T\subset\Omega$ a shape parameter $t >0$. We obtain a lower bound for the area of $T$ in terms of $t$.
{"ft_lang_label":"__label__en","ft_lang_prob":0.62545365,"math_prob":0.90130454,"size":405,"snap":"2019-26-2019-30","text_gpt3_token_len":108,"char_repetition_ratio":0.09975062,"word_repetition_ratio":0.0,"special_character_ratio":0.24197531,"punctuation_ratio":0.07692308,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98853815,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-22T11:37:00Z\",\"WARC-Record-ID\":\"<urn:uuid:f678e09a-92ee-4503-941f-582fa0497e46>\",\"Content-Length\":\"47930\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:81fd2f5c-a45a-4113-965a-f367b1c0f98c>\",\"WARC-Concurrent-To\":\"<urn:uuid:bcc572ea-f297-4c4f-acfb-2a66fa18335e>\",\"WARC-IP-Address\":\"54.241.57.76\",\"WARC-Target-URI\":\"https://www.msri.org/seminars/21302\",\"WARC-Payload-Digest\":\"sha1:FUJV42MEVKJDW3ND6E43WI4IF7JRH2DC\",\"WARC-Block-Digest\":\"sha1:GXCEYOOS4TDKPPSIQ7DVBPR7FMYWUX3S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195528013.81_warc_CC-MAIN-20190722113215-20190722135215-00238.warc.gz\"}"}