Learn Finnish: He tekivät uuden ennätyksen vanhimmalla jäätiköllä. - They made a new record on the oldest glacier.

The basic adjective is vanha (old), and its basic superlative form is vanhin (oldest). When we add the adessive ending -lla, we have to use the superlative's inflectional stem. Because adding -lla closes the syllable, we use the weak superlative stem -imma- or -immä-. Since vanha has back vowels (a, o, u), we use -imma-, making it vanhimma- + -lla = vanhimmalla.

Why is the object uuden ennätyksen instead of the partitive uutta ennätystä?

We use the genitive-like accusative case here because the action was fully completed—they successfully achieved the record. If they were currently in the process of making it, or if it was an ongoing, incomplete action, we would use the partitive case.

Why are we using the adessive ending -llä on jäätiköllä instead of the inessive -ssä?

The adessive case (-lla / -llä) usually translates to 'on' or 'at.' Glaciers (jäätikkö) are treated as open surfaces in Finnish, so you stand on top of them, not inside them.

Why does jäätiköllä have only one k, while its base form has two?